U.S. patent application number 09/826317 was filed with the patent office on 2001-10-11 for image processing method of x-ray ct, x-ray ct and x-ray ct image-taking recording medium.
Invention is credited to Ueno, Yoshihiro, Yamada, Yosihiro.
Application Number | 20010028696 09/826317 |
Document ID | / |
Family ID | 18619476 |
Filed Date | 2001-10-11 |
United States Patent
Application |
20010028696 |
Kind Code |
A1 |
Yamada, Yosihiro ; et
al. |
October 11, 2001 |
Image processing method of X-ray CT, X-ray CT and X-ray CT
image-taking recording medium
Abstract
In an image processing, a high-absorber area is set and
weighting is carried out according to a length of a path through
which X-rays pass in the high-absorber area, so that estimated
image taking data at a portion where X-rays pass through the
high-absorber area in considering a weight is obtained. Measured
projection data at the portion where X-rays pass through the
high-absorber area is replaced by data according to overwriting
estimated projection data obtained by forward projecting the
estimated image to correct and reconstitute the measured projection
data. Thus, there can be obtained a corrected fault image having a
reduced artifact and a high contrast, and considering the weight in
the high-absorber area. Therefore, the artifact formed on the fault
image due to absorption or dispersion of X-rays by an X-ray
high-absorber, such as metal, can be reduced.
Inventors: |
Yamada, Yosihiro;
(Kyoto-shi, JP) ; Ueno, Yoshihiro; (Kusatsu-shi,
JP) |
Correspondence
Address: |
KANESAKA AND TAKEUCHI
1423 Powhatan Street
Alexandria
VA
22314
US
|
Family ID: |
18619476 |
Appl. No.: |
09/826317 |
Filed: |
April 5, 2001 |
Current U.S.
Class: |
378/4 ; 378/207;
378/901 |
Current CPC
Class: |
G06T 11/005 20130101;
Y10S 378/901 20130101 |
Class at
Publication: |
378/4 ; 378/901;
378/207 |
International
Class: |
A61B 006/03 |
Foreign Application Data
Date |
Code |
Application Number |
Apr 7, 2000 |
JP |
2000-106271 |
Claims
What is claimed is:
1. An image processing method for obtaining a fault image by
reconstructing image data obtained by an X-ray CT, comprising: an
image-taking process for obtaining measured projection data by
irradiating X-rays from a circumference of an object to be tested
and detecting the X-rays passing through the object to be tested; a
first image reconstructing process for reconstructing an initial
image by subjecting the measured projection data obtained in said
image-taking process to filtering and then backprojecting the
filtered measured projection data; an estimated image setting
process for setting an estimated image with a predetermined value;
a high-absorber area setting process for setting a high-absorber
area based on the initial image derived from the first image
reconstructing process; an estimated projection data derivation
process for deriving estimated projection data by forward
projecting the estimated image in an X-ray irradiation direction; a
comparison reference image deriving process for deriving a
comparison reference image by backprojecting one of a difference
and a ratio between the estimated projection data and the measured
projection data; a weighting comparison reference image deriving
process for deriving a weighted comparison reference image weighted
such that as a path through which X-rays pass in the high-absorber
area becomes longer, pixel values of the comparison reference image
become smaller; an estimated image overwriting process for
overwriting the estimated image by the weighted comparison
reference image; an overwritten estimated projection data deriving
process for deriving overwritten estimated projection data through
the forward projection of the estimated image overwritten at the
estimated image overwriting process; a measured projection data
correction process for replacing the measured projection data at a
portion where the X-rays pass through the high-absorber area with
data according to the overwritten estimated projection data to
correct the measured projection data; and a second image
reconstructing process for reconstructing an image of the corrected
measured projection data to derive the fault image.
2. An image processing method according to claim 1, wherein after
said estimated image overwriting process, said estimated projection
data derivation process, said comparison reference image deriving
process and said weighting comparison reference image deriving
process are repeated at least once to reduce an artifact according
to the artifact appearing on the estimated image overwritten at the
estimated image overwriting process.
3. An X-ray CT device for obtaining a fault image by reconstructing
image data, comprising: an X-ray irradiation device for irradiating
X-rays from a circumference of an object to be tested to allow the
X-rays to pass through paths in the object; an X-ray detecting
device for obtaining measured projection data by detecting the
X-rays irradiated from the X-ray irradiation device and passing
through the object to be tested; a first image reconstructing
device electrically connected to the X-ray detecting device for
reconstructing an original image by subjecting the measured
projection data obtained by the X-ray detecting device to filtering
and then backprojecting filtered measured projection data; an
estimated image setting device for setting an estimated image with
a predetermined value; a high-absorber area setting device
electrically connected to the first image reconstructing device for
setting a high-absorber area on the measured fault image derived
from the first image reconstructing device; an estimated projection
data deriving device electrically connected to the estimated image
setting device for deriving estimated projection data by forward
projecting the estimated image in an X-ray irradiation direction; a
comparison reference image deriving device electrically connected
to the X-ray detecting device and the estimated projection data
deriving device for deriving a comparison reference image with
pixel values by backprojecting one of a difference and a ratio
between the estimated projection data and the measured projection
data; a weighing comparison reference image deriving device
electrically connected to the comparison reference image deriving
device for deriving a weighted comparison reference image weighted
such that the pixel values in the comparison reference image become
smaller as one of the paths through which the X-rays pass in the
high-absorber area becomes longer; an estimated image overwriting
device electrically connected to the estimated image setting device
and weighing comparison reference image deriving device for
overwriting the estimated image by the weighted comparison
reference image; an overwriting estimated projection data deriving
device electrically connected to the estimated image overwriting
device for deriving overwritten estimated projection data by
forward projecting the overwritten estimated image; a measured
projection data correcting device electrically connected to the
X-ray detecting device and the overwriting estimated projection
data deriving device for correcting the measured projection data by
replacing the measured projection data at a portion through which
the X-rays pass in the high-absorber area by data according to the
overwritten estimated projection data; and a second image
reconstructing device electrically connected to the measured
projection data for deriving the fault image by reconstructing an
image of the corrected measured projection data.
4. An X-ray CT device according to claim 3, further comprising a
repeating operation device electrically connected to the estimated
projection data deriving device for overwriting the estimated image
such that an artifact is reduced by repeatedly carrying out the
processes of the estimated projection data deriving device, the
comparison reference image deriving device, the weighing comparison
reference image deriving device and the estimated image overwriting
device at least two times according to the artifact appearing on
the estimated image overwritten by the estimated image overwriting
device.
5. An X-ray CT image-taking recording medium to be read by a
computer, containing a program for executing the image process
method comprising: an image-taking process for obtaining measured
projection data by irradiating X-rays from a circumference of an
object to be tested and detecting the X-rays passing through the
object to be tested; a first image reconstructing process for
reconstructing a measured initial image by subjecting the measured
projection data obtained in said image-taking process to filtering
and then backprojecting the filtered measured projection data; an
estimated image setting process for setting an estimated image with
a predetermined value; a high-absorber area setting process for
setting a high-absorber area based on the measured fault image
derived from the first image reconstructing process; an estimated
projection data derivation process for deriving estimated
projection data by forward projecting the estimated image in an
X-ray irradiation direction; a comparison reference image deriving
process for deriving a comparison reference image by backprojecting
one of a difference and a ratio between the estimated projection
data and the measured projection data; a weighting comparison
reference image deriving process for deriving a weighted comparison
reference image weighted such that as a path through which X-rays
pass in the high-absorber area becomes longer, pixel values of the
comparison reference image become smaller; an estimated image
overwriting process for overwriting the estimated image by the
weighted comparison reference image; an overwritten estimated
projection data deriving process for deriving overwritten estimated
projection data through the forward projection of the estimated
image overwritten at the estimated image overwriting process; a
measured projection data correction process for replacing the
measured projection data at a portion where the X-rays pass through
the high-absorber area with data according to the overwritten
estimated projection data to correct the measured projection data;
and a second image reconstructing process for reconstructing an
image of the corrected measured projection data to derive the fault
image.
6. An X-ray CT image-taking recording medium according to claim 5,
wherein after said estimated image overwriting process, the
estimated projection data derivation process, the comparison
reference image deriving process and the weighing comparison
reference image deriving process are repeated at least once to
reduce an artifact according to the artifact appearing on the
estimated image overwritten at the estimated image overwriting
process.
Description
BACKGROUND OF THE INVENTION AND RELATED ART STATEMENT
[0001] The invention relates to an image processing method of an
X-ray CT, an X-ray CT, and an X-ray CT image-taking recording
medium, especially, to a technique for reducing a false image or
artifact by absorption or dispersion of X-rays by an X-ray
high-absorber, such as metal.
[0002] Generally, as shown in FIG. 8(a), an X-ray CT includes an
X-ray tube 51 for generating an X-ray beam B and an X-ray detector
52 for detecting X-rays. The X-ray tube 51 and the X-ray detector
52 are disposed to sandwich an object P to be tested, and the X-ray
tube 51 irradiates the X-ray beam B to the object P to be tested to
take images while rotating around an axis Z of the object P (in a
direction extending vertically with respect to a sheet surface in
FIG. 8(a)). Generally, the X-ray detector 52 includes a plurality
of detecting elements CHi (i=1, 2, . . . , n-1, n wherein n is a
natural number), and the detecting elements CHi are disposed in a
fan shape every fine angle. (FIG. 8(a))
[0003] In a conventional image processing method, X-rays are
irradiated from the circumference of the object P to be tested to
obtain X-ray transmission data f(P) on a projection plane U (FIG.
8(b)). Incidentally, in the present specification, the X-ray
irradiation is referred to as "the object P to be tested is
projected in an irradiation direction of the X-ray beam B"
(hereinafter, also abbreviated to "the object P to be tested is
projected"). The X-ray transmission data f(P) obtained on the
projection plane U at this time is also referred to as "measured
projection data f(P)". Further, the measured projection data f(P)
on the projection plane F is subjected to a reconstruction process,
such as filtering and backprojection, to obtain an original image
G[f(P)] on an image plane V (FIG. 8(c)). In the present
specification, the filtering is defined such that a convolution
integral calculus (superposition integral calculus) is carried out
by using a convolution kernel function. Also, the method where the
projection data is subjected to the reconstruction process, such as
filtering and backprojection, is generally known as a filtered
backprojection (hereinafter referred to as FBP) method.
Incidentally, since the FBP method is one of representative
reconstruction processing methods, explanation thereof is omitted.
By the way, derivation of the projection data of an image by using
a mathematical algorithm is called as "forward projecting the image
in an irradiation direction of X-rays" (hereinafter, if applicable,
abbreviated as "forward projecting the image").
[0004] Incidentally, a row of the detecting elements CH, and a row
of angles .theta. in an irradiation direction of X-ray beam B are
shown in a horizontal axial direction and in a vertical axial
direction on the projection plane U, respectively. Also, hatching
areas in the projection plane U and the image plane V are shown
illustratively. Further, the projection plane U and image plane V
show areas. Based on the above, the following explanation is
provided.
[0005] Incidentally, in case a certain object is represented by
"P", the projection of the object P is indicated by f(P); in case a
fault image is represented by ".alpha.", the forward projection of
the fault image a is indicated by F(.alpha.); and in case certain
projection data is represented by ".beta.", the fault image
obtained by filtered and backprojection of the projection data
.beta., i.e. the image reconstituted by the FBP method is indicated
by B[H(.beta.)] or G(.beta.). At this time, it is assumed that an
operation of the backprojection is represented by "B"; an operation
of the filtering is represented by "H"; and an operator of the
backprojection and filtering is represented by "G". Also, in order
to make distinction between the ID projection of the object to be
tested and the forward projection of the image, the symbols with
respect to the projection and the forward projection are
represented by "f" and "F". Further, since there is a measurement
error, in case the projection data .beta. is measured, even if the
fault image obtained by the FBP method of the measured projection
data .beta. is forward projected, the forward projected fault image
does not return to exactly the same data as the originally measured
projection data .beta.. Therefore, in the present specification,
assuming that .beta.=F[G(.beta.)] does not hold, the following
explanation is made. Incidentally, the projection data (including
also the measured projection data f(P)) and the image (including
also the measured fault image G[f(P)]) have numeral weights,
different from the projection plane F and the fault plane G, in
other words, they are dealt as pixel values in the following
explanations of the present specification.
[0006] However, in case of the conventional image process method,
there are the following problems.
[0007] In detail, when a reconstruction of the image is carried out
by taking an image of an object to be tested, false images are
generated. Especially, in case of taking an image of an object to
be tested including a high-absorber consisting of a metal or the
like, the false images generated at and around the high-absorber
become conspicuous due to absorption or dispersion by the
high-absorber. Hereinafter, in the present specification, the
above-explained false image is called as "artifact". In the false
images, especially, there are known streak artifacts where radially
striped patterns are generated around the high-absorber, and
shading artifacts which are generated at portions sandwiched by a
plurality of high-absorbers. In order to reduce the artifacts
including the above-mentioned artifacts, various methods have been
proposed. As representative reducing methods, there are mentioned
an iterative reconstruction and reprojection (hereinafter referred
to as "IRR") method, and algebraic reconstruction
technique/expectation and maximization (hereinafter referred to as
"ART/EM") method.
[0008] First, the IRR method is explained with reference to FIG. 9.
In the IRR method, an original fault image G[f(P)] on the fault
plane V obtained by a conventional image processing method is again
forward projected by a mathematical algorithm in an irradiation
direction of X-rays to obtain forward projection data F(G[f(P)]) on
the projection plane U. Then, an operator sets a portion
corresponding to a high-absorber as a high-absorber area M on the
image plane V with reference to the original fault image G[f(P)] on
the fault plane G ((a) in FIG. 9). Incidentally, the high-absorber
area M is a closed area. A portion L where X-rays pass through the
high-absorber area is formed in the projection plane U. A pixel
value of the measured projection data f(P) with respect to the
portion L where X-rays pass through the high-absorber area is
replaced by a pixel value of the forward projection data F(G[f(P)])
or a pixel value derived from the forward projection data
F(G[f(P)]) to correct the measured projection data f(P) and obtain
a corrected projection data F(P.sub.1). It should be noted that the
forward projection data F(G[f(P)]) is different from the corrected
projection data F(P.sub.1) ((b) in FIG. 9) Further, reconstruction
of the corrected projection data F(P.sub.1) is carried out again to
obtain a corrected fault image G[F(P.sub.1)] on the image plane V.
((c) in FIG. 9)
[0009] Incidentally, "the pixel value of the measured projection
data f(P) of the portion L where X-rays pass through the
high-absorber area is replaced by the pixel value of correcting
forward projection data F(G[f(P)])" means that the corrected
projection data F(P.sub.1) is obtained by following equations (1)
and (2).
[0010] In the portion where X-rays do not pass through the
high-absorber area:
F(P.sub.1)=f(P) (1)
[0011] In the portion L where X-rays pass through the high-absorber
area:
F(P.sub.1)=F(G[f(P)]) (2)
[0012] Incidentally, "the pixel value of the measured projection
data f(P) of the portion L where X-rays pass through the
high-absorber area is replaced by the pixel value derived from the
correcting forward projection data F(G[f(P)])" can be obtained by
equations (3) and (4) mentioned below.
[0013] In the portion where X-rays do not pass through the
high-absorber area:
F(P.sub.1)=f(P) (3)
[0014] In the portion L where X-rays pass through the high-absorber
area:
F(P.sub.1)=.alpha..times.F(G[f(P)]) (4)
[0015] In other words, the pixel value of the measured projection
data f(P) of the portion L where X-rays pass through the
high-absorber area is replaced by a value obtained by multiplying
the forward projection data F(G[f(P)]) of the portion L where
X-rays pass through the high-absorber area at predetermined times
(.alpha. times).
[0016] By the above-stated method, in the portion L through which
X-rays pass in the high absorber area, the pixel value of the
forward projection data F(G[f(P)]) or the pixel value derived from
the forward projection data F(G[f(P)]) passing through the
high-absorber area is utilized, instead of the pixel value of the
measured projection data f(P). Therefore, in the portion where
X-rays do not pass through the high-absorber area, the pixel value
of the measured projection data f(P) is left as it is, while in the
portion L where X-rays pass through the high-absorber area, data
obtained by subjecting to the filtered, backprojection
(reconstruction by the FBP method) process and the forward
projection is replaced therewith. Here, in the portion L where
X-rays passes through the high-absorber area, the correcting
forward projection data F(G[f(P)]) is more accurate than the
measured projection data f(P) as the data. Therefore, in the
corrected projection data F(P.sub.1), the forward projection data
F(G[f(P)]) to reduce the artifact portion is used. However, in the
IRR method, since it is required that the correction data should be
very accurate, the effects are limited and reduction effects are
poor. On the other hand, as a method where the reduction effect of
the artifact is high, there is an ART/EM method.
[0017] Next, the ART/EM method is explained with reference to FIGS.
10 and 11. FIG. 10 is a drawing showing a process for obtaining an
estimated image b.sub.1 by overwriting an initial image b.sub.o one
time; and FIG. 11 is a drawing showing a process for obtaining an
estimated image b.sub.k+1 by further overwriting or amending, one
time, an estimated image b.sub.k obtained by overwriting the
initial image b.sub.o plural times (in this case, k times).
Incidentally, b.sub.o in FIG. 10 is an estimated image initialized
by an arbitrary positive value, and b.sub.1 is an initial image
obtained by overwriting the initial image b.sub.o one time. Also,
b.sub.k in FIG. 11 is an estimated image obtained by overwriting
the estimated image b.sub.o k times, and b.sub.k+1 is an estimated
image obtained by overwriting the estimated image b.sub.o (k+1)
times.
[0018] As shown in FIG. 10, in the specific example of the ART/EM
method, the initial image b.sub.o is set. The initial image b.sub.o
can be set with an arbitrary positive value by an operator. For
example, the pixel values of X-rays on the whole area may be the
same. Then, the operator sets a portion corresponding to the
high-absorber as a high-absorber area M on the image plane V
referring to a measured fault image G[f(P)] on the image plane V
((a) in FIG. 10) Then, a portion L where X-rays pass through the
high-absorber area is formed on the projection plane U. The initial
image b.sub.o is forward projected to obtain estimated projection
data F(b.sub.o) on the projection plane U. Then, the obtained
estimated projection data F(b.sub.o) is compared with the measured
projection data f(P) ((b)in FIG. 10). When compared, the portion L
where X-rays pass through the high-absorber area is disregarded and
not compared. In other words, with respect to a portion where
X-rays do not pass through the high-absorber area, the estimated
projection data F(b.sub.o) is compared with the measured projection
data f(P). This is also applied to the overwritten, described
later, wherein overwriting of the estimated image is carried out
only for the portion where the high-absorber does not exist.
[0019] Incidentally, in the ART method, the measured projection
data f(P) and the estimated projection data F(b.sub.o) are
compared, and a difference of both data is backprojected to obtain
a comparison reference image. With the comparison reference image,
the initial image b.sub.o is overwritten. On the other hand, in the
EM method, a ratio of the measured projection data f(P) with
respect to the estimated projection data F(b.sub.o) is
backprojected to obtain a comparison reference image. In the same
manner, with the comparison reference image, the estimated image
b.sub.o is overwritten. By the above-stated method, the initial
image overwritten one time becomes an estimated image b.sub.1 ((c)
in FIG. 10). With reference to the pixel values of the portion L
where X-rays pass through the high-absorber area, as described
before, comparison of both projection data and overwriting are not
carried out and disregarded. Thus, the data of the pixel values of
the portion L has no definition nor distinction.
[0020] In the same manner as in the overwriting method of the
initial image b.sub.o, the estimated image f(b.sub.1) is compared
with the measured projection data f(P) to overwrite the estimated
image b.sub.1. Thereafter, in the same manner, the initial image is
overwritten plural times to obtain an intended fault image. More
specifically, when the overwriting of the estimated image b.sub.k
is carried out, as shown in FIG. 11, the estimated image f(b.sub.k)
is compared with the measured projection data f(P) to derive or
obtain an estimated image b.sub.k+1.
[0021] In the image obtained by the above-described methods, higher
effects are obtained for reducing the artifact portion when
compared with that of the IRR method. Especially, the reduction
effects of the streak artifact are conspicuous in the ART/EM
method. However, in the ART/EM method, as described before, since
the portion L where X-rays pass through the high-absorber area is
disregarded when the comparison between the projection data and
overwriting is carried out, data regarding the high-absorber is not
defined. Therefore, there is a defect wherein the shapes of the
high-absorber itself and its circumference are not reproduced.
Also, in case the number of times by which the overwritings of the
estimated images are carried out, i.e. repetition times, is small,
only an image having a low contrast can be obtained, which results
in a poor resolution. In order to obtain a high contrast fault
image, the number of times by which the estimated images are
renewed, i.e. repetition times, should be increased.
[0022] In view of the above problems, the present invention has
been made and an object of the invention is to provide an image
processing method of X-ray CT, X-ray CT and X-ray CT image-taking
recording medium for reducing artifact on a fault image caused by
absorption or dispersion by a high-absorber.
[0023] Further objects and advantages of the invention will be
apparent from the following description of the invention.
SUMMARY OF THE INVENTION
[0024] In the ART/EM method, as described above, since the portion
where X-rays pass through the high-absorber area is disregarded,
shapes of the high-absorber itself and the circumference thereof
can not be reproduced. Therefore, the ART/EM method considering the
portion relating to the high-absorber is desired. However, in case
the data of the portion where X-rays pass through the high-absorber
area is used as it is, reduction effects of the artifact can not be
obtained. Therefore, there is considered an ART/EM method wherein
weighting is carried out according to a length through which X-rays
pass in the high-absorber area (hereinafter, abbreviated as
"weighted ART/EM method").
[0025] Also, in the weighted ART/EM method, since the portion where
X-rays pass through the high-absorber is considered, the reduction
effect of the artifact is reduced when the repetition times are
increased. In other words, when the repetition times are it small,
although the artifact portion is reduced, only low contrast image
can be obtained. On the contrary, when the repetition times are
large, although a high contrast image can be obtained, the
reduction effect of the artifact is lowered. However, in the IRR
method, when measured projection data of the portion where X-rays
pass through the high-absorber area is replaced by the forward
projection data with reduced artifact obtained by the weighted
ART/EM method when the number of repetition times is small to
thereby correct the measured projection data, and then a
reconstruction process is further carried out by the FBP method or
ART/EM method to obtain a high contrast image with reduced
artifact.
[0026] Thus, the present inventors had an idea such that in
addition to the combination of the IRR method and the weighted
ART/EM method, further, when a reconstruction process is carried
out by the FBP method or ART/EM method, a corrected image with
reduced artifact can be obtained.
[0027] The present invention based on the above-described knowledge
and information has the following structure.
[0028] In an image processing method according to a first aspect of
the invention, a processing method obtains a fault image by
reconstructing image data obtained when an image is taken by an
X-ray CT. The image processing method includes (1) an image-taking
process wherein measured projection data can be obtained by
irradiating X-rays from a circumference of an object to be tested
and detecting the X-rays passing through the object to be tested;
(2) a first image reconstructing process for subjecting the
measured projection data obtained in the image-taking process to
filtering and then backprojecting to thereby reconstruct an
original image; (3) an initial image setting process for
initializing or setting an estimated image with an arbitrary
positive value; (4) a high-absorber area setting process for
setting a high-absorber area based on the original fault image
derived from the first image reconstructing process; (5) an
estimated projection data derivation process for deriving estimated
projection data by forward projecting the estimated image in an
X-ray irradiation direction; (6) a comparison reference image
deriving process for deriving or obtaining a comparison reference
image by backprojecting a difference or a ratio between the
estimated projection data and the measured projection data; (7) a
weighted comparison reference image deriving process for deriving
or providing a weighted comparison reference image weighted such
that as a path through which X-rays pass in the high-absorber area
becomes longer, the respective pixel values of the comparison
reference image become smaller; (8) an estimated image overwriting
process for overwriting the estimated image by the weighted
comparison reference image; (9) a repeating operation process for
overwriting an estimated image where an artifact is reduced by
repeatedly carrying out, one time or plural times, the above-stated
respective processes from (5) to (8) according to degrees of the
artifact appearing on the estimated image overwritten at the
estimated image overwriting process; (10) an overwritten estimated
projection data deriving process for deriving or providing
overwritten estimated projection data through the forward
projection of the estimated image overwritten at the repeating
operation process; (11) a measured projection data correction
process for replacing the measured projection data of the portion
where X-rays pass through the high-absorber area with the data
according to the overwritten estimated projection data to correct
the measured projection data; and (12) a second image
reconstructing process for reconstructing the image of the
corrected measured projection data to derive the fault image.
[0029] In an X-ray CT according to a second aspect of the
invention, an X-ray CT obtains a fault image by reconstructing
image data obtained when an image is taken by the X-ray CT. The
X-ray CT includes (a) an X-ray irradiation device for irradiating
X-rays from the circumference of an object to be tested; (b) an
X-ray detecting device for obtaining measured projection data by
detecting X-rays passing through the object to be tested by
irradiation of X-rays by the X-ray irradiation device; (c) a first
image reconstructing device for reconstructing the measured fault
image by subjecting the measured projection data obtained by the
X-ray detecting device to filtering and then backprojecting the
filtered measured projection data; (d) an estimated image setting
device for initializing or setting an estimated image with an
arbitrary positive value; (e) a high-absorber area setting device
for setting a high-absorber area based on the measured original
image derived from the first image reconstructing device; (f) an
estimated projection data deriving device for deriving estimated
projection data by forward projecting the estimated image in the
X-ray irradiation direction; (g) a comparison reference image
deriving device for deriving a comparison reference image by
backprojecting a difference or a ratio between the estimated
projection data and the measured projection data; (h) a weighted
comparison reference image deriving device for deriving a weighted
comparison reference image weighted such that the pixel values of
the comparison reference image become smaller as a path through
which X-rays pass in the high-absorber area become longer; (i) an
estimated image overwriting device for overwriting the estimated
image by the weighted comparison reference image; (j) a repeating
operation device for overwriting to an estimated image wherein the
artifact is reduced by repeatedly carrying out processes, one time
or plural times, by the respective devices from (f) to (i)
according to a degree of the artifact appearing on the estimated
image overwriting by the estimated image overwriting device; (k) a
overwritten estimated projection data deriving device for deriving
the overwritten estimated projection data by forward projecting the
estimated image overwritten by the repeating operation device; (l)
a measured projection data correcting device for correcting the
measured projection data by replacing the measured projection data
of the portion where X-rays pass through the high-absorber area by
the data according to the overwritten estimated projection data;
and (m) a second image reconstructing device for deriving a fault
image by reconstructing an image of the corrected measured
projection data.
[0030] In an X-ray CT image-taking recording medium according to a
third aspect of the invention, a computer-readable X-ray CT
image-taking recording medium is obtained, wherein a program for
executing the image process method, mentioned in the first aspect
of the invention, and read by a computer is recorded.
[0031] A function of the invention described in the first aspect is
explained.
[0032] According to the image process method of the invention, by
setting of a high-absorber area, an estimated image considering the
high-absorber area can be obtained. Through comparison of the
measured projection data and estimated projection data obtained by
the forward projection of the estimated image in the X-ray
irradiation direction, a comparison reference image is derived
based on the backprojection of a difference or a ratio between the
data mentioned above. The comparison reference image is weighted
according to the path, i.e. length, through which X-rays pass in
the high-absorber area. Thus, the weighted comparison reference
image is overwritten to an estimated image having the reduced
artifact caused by dispersion or reflection of the high-absorber
area. The overwritten estimated image of the high-absorber area and
overwritten estimated projection data obtained by forward
projecting the overwritten estimated image in the X-ray irradiation
direction have reduced artifact. The measured projection data at
the portion where X-rays pass through the high-absorber area is
replaced by the data according to the overwritten estimated
projection data to reconstruct the measured projection data through
the correction thereof. Thus, a corrected image having a high
contrast and reduced artifact can be obtained.
[0033] According to the invention described in the second aspect,
the method of the invention of the first aspect can be favorably
carried out, so that a corrected image having a reduced artifact
and a high contrast can be obtained.
[0034] According to the invention described in the third aspect,
the method of the invention described in the first aspect is
carried out by a computer to thereby obtain a corrected image
having a reduced artifact and a high contrast.
BRIEF DESCRIPTION OF THE DRAWINGS
[0035] FIG. 1 is a drawing showing a flow until a finally obtained
corrected image is derived or obtained in the present
invention;
[0036] FIG. 2 is a block diagram showing an essential structure of
an X-ray CT of an embodiment;
[0037] FIG. 3 is a block diagram specifically showing an operation
portion and a memory portion;
[0038] FIG. 4 is a flow chart showing a flow from a start of
image-taking until a low contrast image is obtained (first half
portion);
[0039] FIG. 5 is a flow chart showing a flow from a start of
image-taking until the corrected image is obtained (second half
portion);
[0040] FIG. 6 is a drawing specifically showing an ART/EM method
and a weighted ART/EM method;
[0041] FIG. 7(a) is a drawing showing a relationship between
positions of paths through which X-rays pass in a high-absorber and
weights in the weighted ART/EM method;
[0042] FIG. 7(b) is a graph showing weight functions with respect
to path lengths;
[0043] FIGS. 8(a), 8(b) and 8(c) are drawings showing a series of
flows in a conventional image processing method;
[0044] FIG. 9 is a drawing showing a series of flows of an image
processing method in a conventional IRR method;
[0045] FIG. 10 is a drawing showing a method until an estimated
image b.sub.1 can be obtained by overwriting, one time, an
estimated image b.sub.o in a conventional ART/EM method; and
[0046] FIG. 11 is a drawing showing a method until an estimated
image b.sub.k+1 is obtained by further overwriting once the
estimated image b.sub.k which was overwritten plural times in the
conventional ART/EM method.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
[0047] Before the embodiments according to the present invention
are explained, a theory of the invention is explained with
reference to FIG. 1.
[0048] FIG. 1 roughly shows a flow until a final corrected image is
derived in the present invention. First, X-rays are irradiated to
an object P to be tested from the circumference thereof and the
X-rays passing therethrough are detected to thereby obtain a
measured projection data f(P) on a projection plane F. In the
present specification, the process is also referred to "the object
P to be tested is projected in an irradiation direction of the
X-rays", (hereinafter, according to circumstances, briefly
mentioned as "the object P to be tested is projected").
Incidentally, as mentioned in the explanation of the conventional
example, "projection data of a certain image is derived by using
mathematical algorithm" is called "the image is forward projected".
The measured projection data f(P) obtained by projecting the object
P to be tested in the irradiation direction of X-rays is subjected
to a reconstruction process by an FBP method to thereby obtain an
original fault image G[f(P)] on an image plane G. In the present
specification, this process is called as "the measured projection
data f(P) is subjected to filtering to backproject". By the way, in
case the fault image is obtained by subjecting not only the
measured projection data f(P) but also the other projection data to
the reconstruction process by the FBP method, in the present
specification, the process is also called as "the projection data
is subjected to filtering to backproject".
[0049] Next, an initial image b.sub.o is set. The initial image
b.sub.o can be initially set by an operator with an arbitrary
positive value as described above with reference to the
conventional ART/EM method. For example, pixel values of X-rays in
the whole area may be made uniform. Also, an artifact is produced
on the image plane G due to absorption or dispersion of X-rays by a
high-absorber. The operator sets a portion corresponding to the
high-absorber, which causes the artifact, as a high-absorber area M
on the image plane G. Thus, a portion L where X-rays pass through
the high-absorber area M is produced on the projection plane F.
[0050] As shown in FIG. 1, when the initial image b.sub.o is
forward projected, an estimated projection data F(b.sub.o) is
derived on the projection plane F. The measured projection data
f(P) and the estimated projection data F(b.sub.k) (in case no
overwriting is made, the initial projection data is F(b.sub.o)) are
compared with each other to derive a comparison reference image
d.sub.k (in case no overwriting is made, the comparison reference
image is d.sub.o) based on the backprojection of a difference or
ratio between both data. Incidentally, the above estimated
projection data F(b.sub.k) is obtained through the forward
projection of the estimated image b.sub.k which is obtained by
overwriting the initial image b.sub.o by k times. The overwriting
method will be described later in detail. Further, the comparison
reference image d.sub.k (in case no overwriting is made, the
comparison reference image is d.sub.o) is weighted according to a
length where X-rays pass through the high-absorber area to thereby
derive a weighted comparison reference image e.sub.k (in case no
overwriting is made, the weighted comparison reference image is
e.sub.o). The estimated image b.sub.k is overwritten by the
weighted comparison reference image e.sub.k (in case no overwriting
is made, the weighted comparison reference image is e.sub.o) to
obtain an estimated image b.sub.k+1 (in case the initial image
b.sub.o is overwritten, the estimated image is b.sub.1). In other
words, this is an overwriting. The weighted ART/EM method includes
processes from derivation of the initial projection data F(b.sub.o)
to the overwriting to the estimated image b.sub.k+1. The processes
denoted by reference numeral 30 surrounded by broken lines shown in
FIG. 1 correspond to the weighted ART/EM method.
[0051] The overwritten estimated image b.sub.k+1 is forward
projected to obtain an overwritten estimated projection data
F(b.sub.k+1). The pixel values of the measured projection data f(P)
in the portion L where X-rays pass through the high-absorber area
is replaced by the pixel values according to the overwritten
estimated projection data F(b.sub.k+1) to correct the measured
projection data f(P) and derive or obtain a corrected projection
data F(P.sub.2). The IRR method includes the processes until the
derivation of the corrected projection data F(P.sub.2). The
processes denoted by reference numeral 31 surrounded by
single-dotted chain lines shown in FIG. 1 correspond to the IRR
method.
[0052] The corrected projection data F(P.sub.2) is reconstructed by
the FBP method, ART/EM method or the like to obtain a corrected
image P.sub.3. The corrected image P.sub.3 is the finally obtained
corrected image. Incidentally, the image reconstructing method
carried out by the second image reconstructing process or the
second image reconstructing device includes the image
reconstructing method by not only the FBP method but also the
ART/EM method (including the weighted ART/EM method).
[0053] Next, the essential structures and operations of the
embodiment of the X-ray CT according to the present invention are
explained in detail with reference to block diagrams shown in FIGS.
2 and 3. FIG. 2 is a block diagram showing the essential structures
of the X-ray CT of the present embodiment. FIG. 3 is a block
diagram specifically showing inner portions of an operating portion
and a memory portion, respectively.
[0054] Since functions and operations of the X-ray tube 1, X-ray
detector 2 and detection elements CH.sub.1 shown in FIG. 2, in the
X-ray CT of the present embodiment, are the same as those explained
in the prior art section, explanations thereof are omitted. In
addition to the above, the X-ray CT of the present embodiment
includes a control portion 3 including an operation portion 10
(including a central processing unit); an operating portion 4
including a mouse, key board, touch panel and the like for
operating the control portion 3; a data accumulating system (DAS)
7; a fault image display portion or monitor 8; a memory portion 20
for storing coordinates of the projection plane F and the image
plane G, the projection data and pixel values of the fault image;
and a recording medium 25. The X-ray tube 1 corresponds to an X-ray
irradiation device, and the X-ray detector 2 corresponds to the
X-ray detecting device in the present invention.
[0055] An input operation of the operating portion 4 is carried 102
out by an operator. Commands, such as reading out, writing-in and
setting of data, are carried out at an operation portion 10 through
the control portion 3. Also, the recording medium 25 stores a
program for executing the processes of a flow chart shown in FIG. 3
to allow the program to be executed by the control portion 3 built
in the computer. When the program is executed, the control portion
3 writes in and reads out from the memory portion 20 to allow the
operation portion 10 to execute the operation process.
Incidentally, the operating portion 4 includes an initial image
setting portion 5 for initially setting an initial image b.sub.o
with an arbitrary positive value, and a high-absorber area setting
portion 6 for setting a portion corresponding to a high absorber,
as a high-absorber area M, with reference to a measured fault image
G[f(P)]. The pixel values of the initial image b.sub.o and the
coordinates of the high-absorber area M set by the high-absorber
area setting portion 6 are written in the memory portion 20 through
the control portion 3. The initial image setting portion 5
corresponds to an initial image setting device, the high-absorber
area setting portion 6 corresponds to a high-absorber area setting
device, and the recording medium 25 corresponds to an X-ray CT
image-taking recording medium, in the present invention,
respectively. In the present embodiment, the high-absorber area
setting portion 6 is structured such that the operator carries out
the setting. However, the high-absorber area M may be automatically
set according to the pixel values and the like of the measured
fault image G[f(P)].
[0056] On the other hand, the data accumulating system 7 has a
function for collecting the X-ray transmission data f(P) detected
by the X-ray detector 2 as X-ray beams B are irradiated from the
circumference of the object P to be tested. The X-ray transmission
data f(P) collected by the data accumulating system 7, i.e. the
measured projection data f(P), is written in the memory portion 20
through the control portion 3.
[0057] Next, specific structures of the operation portion 10 and
the memory portion 20 are described in detail with reference to
FIG. 3.
[0058] First, the specific structure of the operation portion 10 is
explained. As shown in FIG. 3, the operation portion 10 includes a
forward projection portion 11, reconstruction portion 12,
replacement correction portion 13, comparison reference image
operating portion 14, weighting operation portion 15 and fault
image overwriting portion 16.
[0059] The forward projection portion 11 has a function for forward
projecting a fault image on a image plane G (also including the
high-absorber area M) read out from a fault image memory portion
21, described later, to derive or provide forward projection data
on a projection plane F (also including the L portion where X-rays
pass through the high-absorber area). The forward projection
portion 11 corresponds to an estimated projection data deriving
device and an overwriting estimated projection data deriving device
of the present invention.
[0060] The reconstruction portion 12 has functions for providing
filtering to the forward projection data on the projection plane F
(also including a portion L where X-rays pass through the
high-absorber area) read out from a forward projection data memory
portion 22, described later, and then carrying out the
backprojection to reconstruct so that the fault image is derived on
the image plane G (also including the high-absorber area M). In
other words, the reconstruction portion 12 means a device for
reconstructing the fault image by the FBP method. The
reconstruction portion 12 corresponds to a first image
reconstructing device, and a portion of a second image
reconstructing device (only in case the reconstruction is carried
out by the FBP method) of the present invention.
[0061] The replacement correction portion 13 has a function for
replacing the pixel values or the forward projection data of the
portion L where X-rays pass through the high-absorber area read out
from the forward projection data memory portion 22 with the pixel
values or other forward projection data, or pixel values or data
according to the latter forward projection data to thereby carry
out corrections of the former forward projection data. The
replacement correction portion 13 corresponds to a measured
projection data correction device of the present invention.
[0062] The comparison reference image operating portion 14 has a
function for comparing the forward projection data read out from
the forward projection data memory portion 22 with other forward
projection data to derive a comparison reference image d.sub.k
obtained by backprojecting a difference or ratio between the data.
The comparison reference image operating portion 14 corresponds to
a comparison reference image deriving device of the invention.
[0063] The weighting operation portion 15 has a function for
weighting the comparison reference image d.sub.k read out from the
comparison reference image memory portion 23, described later,
according to a length of an area where X-rays pass through the
high-absorber. More specifically, the weighting is carried out such
that ID as a path through which X-ray passes in the high absorber
becomes longer, the respective pixel values of the comparison
reference image d.sub.k become smaller. The weighting operation
portion 15 corresponds to a weighting comparison reference image
deriving device of the invention.
[0064] The fault image overwriting portion 16 has a function for
overwriting the fault image read out from the fault image memory
portion 21 by the weighted comparison reference image e.sub.k read
out from the comparison reference memory portion 23. The fault
image overwriting portion 16 corresponds to an estimated image
overwriting device of the present invention.
[0065] Next, a specific structure of the memory portion 20 is
explained. The memory portion 20, as shown in FIG. 3, includes a
fault image memory portion 21, a forward projection data memory
portion 22 and a comparison reference image memory portion 23.
[0066] The fault image memory portion 21 has writing and reading
functions such that respective coordinates and pixel values of the
fault image on the image plane G obtained from the reconstruction
portion 12 and the fault image overwriting portion 16, the
coordinates of the high-absorber area M set by the high-absorber
area setting portion 6 and respective coordinates and pixel values
of the initial image b.sub.o on the image plane G set by the
estimated image setting portion 5 are written therein. If
necessity, in other words, according to a reading command of the
operating portion 4, respective coordinates and pixel values of the
original image on the image plane G are read through the control
portion 3. Incidentally, the read-out initial image on the image
plane G is displayed on the fault image display portion 8. Then,
the pixel values of the initial image are allowed to correspond to
colors on the screen of the fault image display portion 8. For
example, in case the pixel values of the initial image are small,
the color on the screen is made lighter, and in case the pixel
values of the initial image are large, the color on the screen is
made darker so that shadings according to the pixel values are
displayed on the fault image display portion or monitor 8.
[0067] The forward data memory portion 22 has writing and reading
functions such that the respective coordinates and pixel values of
X-ray transmission data f(P) (measured projection data f(P)) of the
object P to be tested on the projection plane F collected by the
data accumulating system 7 and the respective coordinates and pixel
values of the forward projection data on the projection plane F
obtained from the forward projection portion 11 and the replacement
correction portion 13 are written therein, and if necessity, the
respective coordinates and pixel values of the forward projection
data on the projection plane F are read. Incidentally, in the
present embodiment, the respective coordinates and pixel values of
the forward projection data on the projection plane F are not
displayed on the monitor. However, the respective coordinates and
pixel values of the read-out forward projection data on the
projection plane F may be displayed on a monitor for the forward
projection data, or a superposition display may be made on the
fault image display portion or monitor 8.
[0068] The comparison reference image memory portion 23 has writing
and reading functions such that the pixel values of a comparison
reference image d.sub.k obtained from the comparison reference
image operating portion 14 and the pixel values of a weighted
comparison reference image e.sub.k obtained from the weighing
operation portion 15 are written therein, and if necessary, the
pixel values of the comparison reference images thereof are
read.
[0069] Next, a series of operations from the start of taking the
image to obtaining a corrected image by the image processing method
and the X-ray CT image-taking recording medium of the X-ray CT
having the structure as described above are explained with
reference to flow charts as shown in FIGS. 4 and 5 and the weighed
ART/EM method as shown in FIGS. 6, 7(a) and 7(b). FIG. 4 is a first
half of the flow chart showing a flow from the start of taking the
image to obtaining the fault image. FIG. 5 is a latter half of the
flow chart showing the flow from the start of taking the image to
obtaining the corrected image. FIG. 6 is a diagram showing the
ART/EM method and the weighed ART/EM method in tail. FIG. 7(a) is a
diagram showing a relationship between the positions of paths
passing through the high-absorber and weights, and FIG. 7(b) is a
graph showing a relationship between weight functions and path
lengths.
[0070] (Step S1) The X-ray transmission data f(P) of an object P to
be tested which is collected by the data accumulating system (DAS)
7 is written in the forward projection data memory portion 22
through the control portion 3 as measured projection data f(P).
Collection of the measured projection data f(P) corresponds to an
image-taking process of the present invention.
[0071] (Step S2) The measured projection data f(P) read from the
forward projection data memory portion 22 is reconstructed by the
reconstruction portion 12. The reconstructed initial image is
derived as the measured fault image G[f(P)] to be written in the to
fault image memory portion 21. Incidentally, the written-in
measured fault image G[f(P)] is read from the fault image memory
portion 21 through the control portion 3 to be displayed on the
fault image display portion or monitor 8. The derivation and
display of the measured fault image G[f(P)] correspond to a first
image reconstruction process.
[0072] (Step S3) An estimated image b.sub.o is initially set with a
suitable or predetermined value by an operator through an input
operation of an operating portion 4 including a mouse, keyboard,
touch panel and the like. When the initial image b.sub.o is set,
the initial image is written in the fault image memory portion 21
through the control portion 3 from the estimated image setting
portion 5 in the operating portion 4. The setting of the initial
image b.sub.o corresponds to an estimated image setting process of
the present invention.
[0073] (Step S4) The operator sets the high-absorber area M based
on the measured fault image G[f(P)] through an input operation of
the operating portion 4. When the high-absorber area M is set, the
high-absorber area M is written in the fault image memory portion
21 through the control portion 3 from the high-absorber area
setting portion 6 in the operating portion 4. The operator sets a
portion which causes an artifact as the high-absorber area M. In
other words, the operator sets the portion corresponding to the
high-absorber as the high-absorber area M with reference to the
measured fault image G[f(P)] on the image plane G displayed on the
fault image display portion 8. Incidentally, the high-absorber area
M may be directly set into the fault image display portion or
monitor 8 through the input operation of the operating portion 4
including the mouse, keyboard, touch panel and the like. The
setting of the high-absorber area M corresponds to a high-absorber
area setting process of the present invention.
[0074] (Step S5) The initial image b.sub.o read out from the fault
image memory portion 21 is forward projected by the forward
projection portion 11. The forward projected data is derived on the
projection plane F as the initial projection data F(b.sub.o) to be
written in the forward projection data memory portion 22. At this
time, the portion L where X-rays pass through the high-absorber
area is formed on the projection plane F, and the respective
coordinates of the portion L where X-rays pass through the
high-absorber area are also written in the forward projection data
memory portion 22. The derivation of the initial projection data
F(b.sub.o) corresponds to an estimated projection data derivation
process of the present invention.
[0075] (Step S6) The comparison reference image operation portion
14 compares the initial projection data F(b.sub.o) read from the
forward projection data memory portion 22 and the measured
projection data f(P) to derive or provide a comparison reference
image d.sub.o through backprojection for a difference or ratio
between the both data. The derived comparison reference image
d.sub.o is written in the comparison reference image memory portion
23. The derivation of the comparison reference image do corresponds
to a comparison reference image derivation process of the present
invention. Next, the derivation of the comparison reference image
d.sub.o is explained together with the conventional ART/EM
method.
[0076] In case an X-ray beam B is irradiated in a direction of an
angle .theta..sub.j from the X-ray tube 1, as shown in FIG. 6,
measured projection data f(P.sub.j) can be obtained on the
projection plane F as the projection data, and at the same time, an
image B[f(P.sub.j)] is formed on the image plane G as a
reconstruction image. The image B[f(P.sub.j)] is obtained by
backprojecting the measured projection data f(P.sub.j) and is not
subjected to the filtering. The coordinates of the X-ray
transmission data detected by a certain detection element CH.sub.i
correspond to the coordinates (CH.sub.i, .theta..sub.j) on the
projection plane F. In the same manner, on the image plane G, there
is formed a locus line H passing through a section of the object P
to be tested and the detection element CH.sub.i in a direction of
angle .theta..sub.j. It is assumed that a pixel value of the
coordinates (CH.sub.i, .theta..sub.j) on the projection plane F
relative to the measured projection data f(P.sub.j) is f(P.sub.ij)
and a pixel value of the coordinates (CH.sub.i, .theta..sub.j) on
the projection plane F relative to the estimated projection data
F(b) is F(b.sub.ij). At this time, in order to bring the pixel
value F(b.sub.ij) of the coordinates (CH.sub.i, .theta..sub.j) on
the projection plane F relative to the estimated projection data
F(b) close to the pixel value f(P.sub.ij) of the coordinates
(CH.sub.i, .theta..sub.j) on the projection plane F relative to the
measured projection data f(P.sub.j), in the ART method, a
difference f(P.sub.ij)-F(b.sub.ij) as an addition value is added to
the pixel value F(b.sub.ij) of the coordinates (CH.sub.i,
.theta..sub.j), while in the EM method, the pixel value F(b.sub.ij)
of the coordinates (CH.sub.i, .theta..sub.j) is integrated by a
ratio f(P.sub.ij)/F(b.sub.ij) as an integration value. The addition
value f(P.sub.ij)-F(b.sub.ij) or integration value
f(P.sub.ij)/F(b.sub.ij) is backprojected and divided by a pitch
number N to obtain a comparison reference image. In the ART method,
an overwritten estimated image becomes a sum of the estimated image
prior to its overwriting and the comparison reference image, while,
in the EM method, the overwritten estimated image becomes a product
of the estimated image prior to its overwriting and the comparison
reference image. Incidentally, in the present specification, the
pitch number N is defined to be a value obtained by dividing the
whole angle of the X-ray tube 1 and the X-ray detector 2 rotated
when the CT image-taking is carried out by the rotated angle of the
X-ray tube 1 and the X-ray detector 2 when one measurement is
carried out. For example, in case the whole rotated angle of the
X-ray tube 1 and X-ray detector 2 is 360.degree. when the CT
image-taking is carried out and the one measurement is carried out
with 1.degree. pitch by the X-ray tube 1 and the X-ray detector 2,
the pitch number N can be obtained as 360.degree./1.degree.=360.
The reason why the pitch number N is calculated based on
per-unit-pitch-number is that in case the pitch number of rotation
for the one measurement is different, a weight of the overwritten
image is changed.
[0077] Also, in case F(b.sub.ij) is changed to f(P.sub.ij), as
shown in FIG. 6, the image is changed altogether to the portion of
the locus line H on the fault plane G. Therefore, repetition is
required until the image converges. Also, in the conventional
ART/EM method, as described above, with respect to only the portion
which does not pass through the high-absorber area, the measured
projection data and the estimated projection data are compared and
overwritten.
[0078] From the above, with reference to the portion which does not
pass through the high-absorber area, according to the ART method,
the comparison reference image d.sub.k is represented by equation
(5); and according to the EM method, the comparison reference image
d.sub.k is represented by equation (6), as described blow:
d.sub.k=1/N.times.B[f(P)-F(b.sub.k)] (ART method) (5)
d.sub.k=1/N.times.B[f(P)/F(b.sub.k)] (EM method) (6)
[0079] Therefore, in case of the conventional ART/EM method, the
overwritten estimated image b.sub.k+1 can be obtained, as below
mentioned equations (7) and (8), by using the estimated image
b.sub.k and the comparison reference image d.sub.k prior to the
overwriting.
b.sub.k+1=b.sub.k+d.sub.k (ART method) (7)
b.sub.k+1=b.sub.k.times.d.sub.k (EM method) (8)
[0080] As described above, in equation (7) of the ART method, the
overwritten estimated image b.sub.k+1 becomes a sum of the
estimated image b.sub.k and comparison estimated image d.sub.k
prior to the overwriting. In equation (8) for the EM method, the
overwritten estimated image b.sub.k+1 becomes a product of the
estimated image b.sub.k and the comparison reference image d.sub.k
prior to the overwriting. However, it should be noted that the
above overwritten estimated image b.sub.k+1 was overwritten
according to the conventional ART/EM method, and overwritten
estimated image b.sub.k+1 according to the weighted ART/EM method,
described later, is different therefrom.
[0081] (Step S7) According to a length of the path through which
X-ray passes in the high-absorber, weighting of the comparison
reference image d.sub.o is carried out to derive a weighted
comparison reference image e.sub.o. When the weighting of the
comparison reference image d.sub.o is carried out, the comparison
reference image d.sub.o read out from the comparison reference
image memory portion 23 is weighted by the weighting operation
portion 15. The weighted comparison reference image e.sub.o is
written in the comparison reference image memory portion 23. The
derivation of the weighted comparison reference image e.sub.o
corresponds to a weighted comparison reference image derivation
process of the present invention. Next, derivation of the weighted
comparison reference image e.sub.o is explained together with the
weighted ART/EM method.
[0082] In order to carry out weighting for an artifact portion, a
weight function W(L) is introduced as shown in FIG. 7(b). The
weight function W(L) is a function with respect to a length L of a
path through which X-ray passes in the high-absorber. The
relationship between a position of the path and a weight is shown
in FIG. 7(a). More specifically, in case X-rays do not pass through
the high-absorber area and the length of the path is denoted as
L.sub.o, L.sub.o becomes 0 and W(L.sub.o) becomes 1. In case X-ray
passes through the high-absorber area and its path length is
L.sub.1, W(L.sub.1) becomes less than 1. Also, in case X-ray passes
through the high-absorber area, its path length is L.sub.2 and the
path length L.sub.2 is larger than the path length L.sub.1, in
other words, in case the transmission area of the high-absorber is
longer than L.sub.1, W(L.sub.2) is smaller than W(L.sub.1). From
the above, 0=L.sub.o<L.sub.1,<L.sub.2 and
1=W(L.sub.o)>W(L.sub.1)>W(L.su- b.2) are satisfied. In other
words, as the transmission area of the high-absorber becomes
longer, absorption or dispersion of the high-absorber becomes
larger and the artifact due to the absorption or dispersion become
large, which means that the weight becomes light. Conversely, as
the transmission area of the high absorber becomes shorter, the
artifact due to the absorption or dispersion becomes smaller, which
means that the weight becomes heavy. Next, derivations of the
weighted comparison reference image e.sub.o and the overwritten
estimated image b.sub.1 are explained by using the equation of the
weight function W(L) (hereinafter, if applicable, abbreviated as
"W").
[0083] In case the projection data is represented by .beta. and a
backprojection considering the weighting (hereinafter, if
applicable, abbreviated as "weighted backprojection") is
represented by B.sub.1(.beta.), the weighting function W,
backprojection B(.beta.) and weighted backprojection
B.sub.1(.beta.) are expressed by following equation (9).
B.sub.1(.beta.)=B(W.beta.).times.Const. (9)
[0084] Incidentally, "Const." is a constant. The value obtained
through the weighted backprojection is different from the original
value obtained through the normal backprojection. Therefore, in
order to make the same value as the original value, the constant is
multiplied.
[0085] From the above, when considering the whole area including
the portion L where X-rays pass through the high-absorber area, the
weighted comparison reference image e.sub.k, according to the ART
method, is expressed by equation (10), and according to the EM
method, it is expressed by equation (11), as follows:
e.sub.k=1/N.times.B.sub.1[f(P)-F(b.sub.k)]=Const./N.times.B(W.times.[f(P)--
F(b.sub.k)]) (ART method) (10)
e.sub.k=1/N.times.B.sub.1[f(P)/F(b.sub.k)]=Const./N.times.B(W.times.[f(P)/-
F(b.sub.k)]) (EM method) (11)
[0086] Therefore, in case of the weighted ART/EM method, the
overwritten estimated images b.sub.k+1 can be obtained from below
mentioned equations (12) and (13) by using the estimated image
b.sub.k and weighted comparison reference image e.sub.k prior to
the overwriting.
b.sub.k+1=b.sub.k+e.sub.k (ART method) (12)
b.sub.k+1=b.sub.k.times.e.sub.k (EM method) (13)
[0087] However, it should be noted that the above overwritten
estimated image b.sub.k+1 is overwritten by the weighted ART/EM
method and is different from the overwritten estimated image
b.sub.k+1 overwritten according to the conventional ART/EM method
described before.
[0088] (Step S8) The initial image b.sub.o read out from the fault
image memory portion 21 is overwritten by the weighted comparison
reference image e.sub.o read out from the comparison reference
image memory portion 23. In other words, the initial image b.sub.o
is overwritten by the fault image overwriting portion 16, i.e. the
above-mentioned weighted ART/EM method. The overwritten estimated
image is obtained as the estimated image b.sub.1 to be written in
the fault image memory portion 21. Incidentally, the written-in
overwritten estimated image b.sub.o is read out from the fault
image memory portion 21 through the control portion 3 to be
displayed on the fault image display portion or monitor 8. The
derivation and display of the overwritten estimated image b.sub.1
correspond to the estimated image overwriting process of the
present invention.
[0089] (Step S9) With reference to the overwritten estimated image
b.sub.1 displayed on the fault image display portion 8, the
operator determines whether the overwritten estimated image b.sub.1
becomes a corrected image for reducing the artifact. Here, the
aforementioned corrected image may have a low contrast. In case it
is determined that the overwritten estimated image b.sub.1 becomes
the aforementioned corrected image, the process advances to Step
10. In case it is determined that the overwritten estimated image
b.sub.1 does not become the aforementioned corrected image, the
process returns to Step S5 to repeat the process from Step 5 to
Step S9 to overwrite the estimated image b.sub.1 in the same manner
as in the overwriting of the initial image b.sub.o. Thereafter,
until it is determined that the overwritten estimated image b.sub.1
becomes a corrected image for reducing the artifact, the process
from Step S5 to Step S9 are repeated to obtain the comparison
reference image d.sub.k, weighted comparison reference image
e.sub.k and the estimated image b.sub.k+1 which is obtained by
further overwriting one time, from the estimated image b.sub.k
(overwriting of k times). Incidentally, repetition of the processes
from Step S5 to Step S9 corresponds to a repeating operation
process of the present invention.
[0090] In case the number of repetition is small, when compared
with the conventional ART/EM method, the estimated image b.sub.k+1
obtained by the above weighted ART/EM method has a reproducibility
for a shape of the high-absorber itself and its circumferential
portion, and an effect for reducing the artifact though it has a
low contrast.
[0091] As described before, in case the number of repetition of the
processes from Step S5 to Step S9 (overwriting times), i.e. the
number of the repetition time, is small, the estimated image
b.sub.k+1 becomes a corrected image having a high reducing effect
for reducing the artifact though the image has a low contrast. On
the contrary, in case the number of repetition time is large,
though the estimated image b.sub.k+1 has a high contrast, the image
becomes a corrected image having a low artifact reducing effect.
However, by combining the IRR method including steps S10 and S11,
for the portion where X-rays pass through the high-absorber area,
the measured projection data f(P) is replaced by an overwritten
estimated projection data F(b.sub.k+1) obtained by the weighted
ART/EM method in case of a small repetition time to correct the
measured projection data. Further, a reconstruction process is
carried out by the FBP method or the ART/EM method to thereby
obtain a high contrast image with reduced artifact. When compared
with only the weighted ART/EM method, in order to obtain an image
having a high contrast of the same degree, its repetition time as
well as the artifact (including the shading artifacts) can be
reduced.
[0092] (Step S10) The estimated image b.sub.k+1 obtained at Step S9
is forward projected by the forward projection portion 11. The
forward-projected data is derived as an overwritten estimated
projection data F(b.sub.k+1) to be written in the forward
projection data memory portion 22. The derivation of the
overwritten estimated projection data F(b.sub.k+1) corresponds to
an overwritten estimated projection data deriving process of the
present invention.
[0093] (Step S11) The replacement correction portion 13 corrects
the measured projection data f(P) to derive the corrected
projection data F(P.sub.2) by using the measured projection data
f(P) and overwritten estimated projection data F(b.sub.k+1) read
out from the forward projection data memory portion 22. The derived
corrected projection data F(P.sub.2) is again written in the
forward projection data memory portion 22. More specifically, for
the portion L where X-rays pass through the high-absorber area, the
pixel values of the measured projection data f(P) are replaced by
pixel values according to the overwritten estimated projection data
F(b.sub.k+1) read from the forward projection data memory portion
22 to correct the measured projection data f(P). The derivation of
the corrected projection data F(P.sub.2) corresponds to a measured
projection data correction process of the present invention. Next,
a method for deriving the corrected projection data F(P.sub.2) by
correcting the measured projection data f(P) is explained in
detail.
[0094] As an example for replacing the pixel values of the
above-mentioned measured projection data f(P) with the pixel values
according to the overwritten estimated projection data F(b.sub.k+1)
read out from the forward projection data memory portion 22 for the
portion L where X-rays pass through the high-absorber area, there
is a method for using therein the overwritten estimated projection
data F(b.sub.k+1) as they are for only the portion L where X-rays
pass through the high-absorber area. In that case, the corrected
projection data F(P.sub.2) can be obtained by equations (14) and
(15) mentioned below.
[0095] In the portion where X-rays do not pass through the
high-absorber area:
F(P.sub.2)=f(P) (14)
[0096] In the portion L where X-rays pass through the high-absorber
area:
F(p.sub.2)=F(b.sub.k+1) (15)
[0097] In the embodiment, although the overwritten estimated
projection data F(b.sub.k+1) for only the portion L where X-rays
passes through the high-absorber area is used as they are, they may
be replaced by the values obtained by multiplying for predetermined
times, the respective overwritten estimated projection data
F(b.sub.k+1) for only the portion L where X-rays pass through the
high-absorber area. For example, in case of replacing with a value
F(b.sub.k+1) obtained by multiplying .alpha. times to satisfy
0<.alpha.<1, above equation (14) can be replaced as equation
(16).
[0098] In the portion where X-rays do not pass through the
high-absorber area:
F(P.sub.2)=.alpha..times.F(b.sub.k+1) (16)
[0099] When the replacement as shown by equation (16) is carried
out, there can be obtained projection data where the artifact is
further reduced.
[0100] (Step S12) The corrected projection data F(P.sub.2) read out
from the forward projection data memory portion 22 is reconstructed
at the reconstruction portion 12. The reconstructed corrected image
is derived as a corrected image P.sub.3 finally obtained in the
present invention to be written in the fault image memory portion
21. Or, the corrected projection data F(P.sub.2) may be again
subjected to the reconstruction process by the weighted ART/EM
method at the comparison reference image operating portion 14,
weighing operation portion 15 and the fault image overwriting
portion 16 to derive the corrected image P.sub.3 which is finally
obtained. The derivation of the corrected image P.sub.3 corresponds
to a second image reconstruction process of the present invention.
In other words, as described before, the final corrected image is
derived through the reconstruction process by the FBP method,
ART/EM method or the like.
[0101] Through the above-stated steps, in the image processing
method and the X-ray CT having the X-ray CT image-taking recording
medium, effects as described below can be obtained. That is, by the
weighted ART/EM method which reduces the repeating time, the
weighting is carried out by considering the data for the portion L,
where X-rays pass through the high-absorber area. Therefore, there
can be obtained the correct image where the high-absorber and its
circumferential portion are reproduced in spite of a low contrast
and the artifact is reduced. Also, the false image of the object to
be tested can be corrected by the IRR method by using the fault
image obtained by the weighted ART/EM method where the number of
repeating time is reduced, and the fault image of the object to be
tested. From the method described before, since the data obtained
for the high-absorber portion become more accurate than the
correction data obtained by the normal IRR method, effects thereof
are not limited. Also, in case an image having the same degree of
the contrast as that of the image obtained by the weighted ART/EM
method is obtained, the number of repeating time as well as the
artifacts (also including a shading artifact) can be reduced.
[0102] As described in detail hereinabove, according to the image
processing method of the X-ray CT of the first aspect of the
invention, the correct image having the high contrast and reduced
artifact can be obtained by replacing the measured projection data
at the portion where X-rays pass through the high-absorber area
with the data according to weighted overwritten estimated
projection data to thereby correct and reconstitute the measured
projection data.
[0103] According to the X-ray CT of the second aspect of the
invention, the correct image having the high contrast and reduced
artifacts can be obtained since the X-ray CT can be preferably
carried out by the first aspect of the invention.
[0104] According to the X-ray CT image-taking recording medium of
the third aspect of the invention, the correct image having reduced
artifact and the high contrast can be obtained by carrying out the
method of the first aspect of the invention with a computer.
[0105] While the invention has been explained with reference to the
specific embodiments of the invention, the explanation is
illustrative and the invention is limited only by the appended
claims.
* * * * *