U.S. patent application number 09/912137 was filed with the patent office on 2002-02-07 for x-ray computed tomography apparatus.
This patent application is currently assigned to Siemens Aktiengesellschaft. Invention is credited to Reinwand, Mario, Stierstorfer, Karl.
Application Number | 20020015476 09/912137 |
Document ID | / |
Family ID | 7650115 |
Filed Date | 2002-02-07 |
United States Patent
Application |
20020015476 |
Kind Code |
A1 |
Reinwand, Mario ; et
al. |
February 7, 2002 |
X-ray computed tomography apparatus
Abstract
In an X-ray computed tomography apparatus with retrospective
beam hardening correction, an overall image of a body slice under
examination is determined from overall attenuation values that are
obtained from the body slice. At least one partial image that shows
essentially only one body substance, such as bone substance, is
extracted from this overall image. Attenuation partial values are
employed for determining a correction value. The attenuation values
are determined for each overall attenuation value from the at least
one partial image by re-projection. A correction value is derived
from the beam hardening error that is determined for a material
combination of two different reference materials.
Inventors: |
Reinwand, Mario; (Steinbach,
DE) ; Stierstorfer, Karl; (Erlangen, DE) |
Correspondence
Address: |
SCHIFF HARDIN & WAITE
6600 SEARS TOWER
233 S WACKER DR
CHICAGO
IL
60606-6473
US
|
Assignee: |
Siemens Aktiengesellschaft
|
Family ID: |
7650115 |
Appl. No.: |
09/912137 |
Filed: |
July 25, 2001 |
Current U.S.
Class: |
378/4 ;
378/18 |
Current CPC
Class: |
A61B 6/583 20130101;
Y10S 378/901 20130101; A61B 6/032 20130101 |
Class at
Publication: |
378/901 ; 378/4;
378/18 |
International
Class: |
A61B 006/03 |
Foreign Application Data
Date |
Code |
Application Number |
Jul 25, 2000 |
DE |
10036142.0 |
Claims
We claim as our invention:
1. An X-ray computed tomography apparatus comprising: a
radiator/detector arrangement that supplies respective sets of
measured intensity values for X-ray projections of a body slice of
a patient, each measured intensity value of each set representing
an intensity of the X-rays after penetration of the body slice in a
partial projection region of an overall projection region; and an
electronic evaluation and reconstruction unit connected to the
radiator/detector arrangement for a) determining an overall
attenuation value for each of the measured intensity values, said
overall attenuation value representing an actual overall
attenuation of the X-rays in the body slice in the appertaining
partial projection region; b) reconstructing an overall image of
the body slice proceeding from the overall attenuation values; c)
extracting a first partially image of a first substance of the body
slice from said overall image; d) determining a respective first
attenuation partial value from said first partial image for each
partial region of the respective X-ray projection, each first
attenuation partial value being a criterion for attenuation of the
X-rays in the appertaining projection partial region in the first
substance of the body slice, and allocating said first attenuation
partial value to the overall attenuation value of the corresponding
partial region; e) extracting a second partial image from said
overall image of a second substance in the body slice; f)
determining a respective second attenuation partial value from said
second partial image for each partial region of the respective
X-ray projection, each second attenuation partial value being a
criterion for attenuation of the X-rays in the appertaining
projection partial region in the second substance of the body
slice, and allocating said second attenuation partial value to the
overall attenuation value of the corresponding partial region; g)
determining a correction value for each overall attenuation value
from the first and second attenuation partial values from
predetermined beam-hardening correction information stored in the
evaluation and reconstruction unit; h) determining an overall
attenuation value corrected for beam hardening for each overall
attenuation value according to the equation:
g.sub.corr=g+k(t.sub.1, t.sub.2) wherein g.sub.corr is the overall
attenuation value corrected for beam hardening, g is the overall
attenuation value, t.sub.1 is the first attenuation partial value,
t.sub.2 is the second attenuation partial value and k(t.sub.1,
t.sub.2) is the correction value determined from t.sub.1 and
t.sub.2, and for determining the correction value k (t.sub.1,
t.sub.2), said evaluation and reconstruction unit i) determining a
set of reference overall attenuation values g.sub.ref (s.sub.1,
s.sub.2) for a material sequence composed of a first reference
material and a second reference material different therefrom for
different thickness combinations, each reference overall
attenuation value g.sub.ref of the set representing the overall
attenuation of the X-rays for a specific thickness combination of
the material sequence; j) calculating a theoretical linear
attenuation of the X-rays for each thickness of the first reference
material from the thickness combinations of the material sequence
represented by a first individual attenuation value s.sub.1; k)
calculating a theoretical linear attenuation of the X-rays for each
thickness of the second reference material from the thickness
combinations of the material sequence represented by a second
individual attenuation value s.sub.2; and l) determining the
correction value for each thickness combination of the material
sequence according to the equation k(t.sub.1,
t.sub.2)=t.sub.1+t.sub.2-g.sub.ref(s.sub.1=t.s- ub.1,
s.sub.2=t.sub.2), wherein g.sub.ref (s.sub.1=s.sub.2=t.sub.2) is
the reference overall attenuation value for a thickness combination
of the material sequence for which s.sub.1=t.sub.1 and
s.sub.2=t.sub.2.
2. A computed tomography apparatus as claimed in claim 1 wherein
the evaluation and reconstruction unit extracts substantially only
image parts of the overall image that correspond to a bone
structure in the body slice in one of the two partial images.
3. A computed tomography apparatus as claimed in claim 2 wherein
the evaluation and reconstruction unit extracts substantially only
image parts of the overall image that correspond to a soft tissue
substance in the body slice in the other of the two partial
images.
4. A computed tomography apparatus as claimed in claim 1 wherein,
for determining the beam hardening correction information, the
evaluation and reconstruction unit stores a function u(x) dependent
on a variable x, which allocates a function value u(x) to each
value of x, with x=A(Bs.sub.1+Cs.sub.2).sub.1 said function value
substantially corresponding to a difference between a sum of the
respective, two individual attenuation values and the respective
reference overall attenuation value, wherein A, B and C are
constants; and wherein the evaluation and reconstruction unit
determines the correction value according to the equation:
k(t.sub.1, t.sub.2)=u(x=A(Bt.sub.1+Ct.sub.2)).
5. An X-ray computed tomography apparatus comprising: a
radiator/detector arrangement that supplies respective sets of
measured intensity values for X-ray projections of a body slice of
a patient under examination, each measured intensity value of the
set representing an intensity of X-rays after penetration of the
body slice in a partial projection region of an overall projection
region; and an electronic evaluation and reconstruction unit
connected to the radiator/detector arrangement for a) determining
an overall attenuation value for each of the measured intensity
values, said overall attenuation value representing an actual
overall attenuation of the X-rays in the body slice in the
appertaining partial projection region; b) reconstructing an
overall image of the body slice proceeding from the overall
attenuation values; c) extracting a partial image of a selected
substance of the body slice from said overall image; d) determining
an attenuation partial value from said partial image for each
partial region of the respective X-ray projection, said attenuation
partial value being a criterion for the attenuation of the X-rays
in the appertaining projection partial region in the selected
substance of the body slice, and allocating said attenuation
partial value to the overall attenuation value of the corresponding
partial region; e) determining a correction value for each overall
attenuation value from the attenuation partial value from
predetermined beam-hardening correction information stored in the
evaluation and reconstruction unit; f) determining an overall
attenuation value corrected for beam hardening for each overall
attenuation value according to the equation: g.sub.corr=g+k(t)
wherein g.sub.corr is the overall attenuation value corrected for
beam hardening, g is the overall attenuation value, t is the
attenuation partial value, and k(t) is the correction value
determined from t.sub.1 and, for determining the correction value k
(t), said evaluation and reconstruction unit g) determining a set
of reference overall attenuation values for a material sequence
composed of a first reference material and a second reference
material different therefrom for different thickness combinations,
each reference overall attenuation value g.sub.ref of the set
representing the overall attenuation of the X-rays for a specific
thickness combination of the material sequence; h) calculating a
theoretical linear attenuation of the X-rays for each thickness of
the first reference material from the thickness combinations of the
material sequence represented by a first individual attenuation
value s.sub.1; i) calculating a theoretical linear attenuation of
the X-rays for each thickness of the second reference material from
the thickness combinations of the material sequence represented by
a second individual attenuation value s.sub.2; and j) determining
the correction value for each thickness combination of the material
sequence according to the equation k(g, t)=t+s.sub.2+g.sub.ref(s-
.sub.1=t, s.sub.2), wherein g.sub.ref (s.sub.1=t, s.sub.2) is the
reference overall attenuation value for a thickness combination of
the material sequence for which s.sub.1=t given s.sub.2 and, for
which g.sub.ref(s.sub.1=t, s.sub.2).
6. A computed tomography apparatus as claimed in claim 5 wherein,
for determining the beam hardening correction information, the
evaluation and reconstruction unit stores a function v(y) dependent
on a variable y which allocates a function value v(y) to each value
of y, with y=D(Eg.sub.ref30 Fs.sub.1), said function value
substantially corresponding to a difference between a sum of the
respective, two individual attenuation values and the respective
reference overall attenuation value, wherein D, E and F are
constants; and wherein the evaluation and reconstruction unit
determines the correction value according to the equation k(g,
t)=v(y=D(Eg+Ft)).
7. A computed tomography apparatus as claimed in claim 5 wherein
the evaluation and reconstruction unit extracts substantially only
image parts of the overall image that correspond to a bone
structure in the body slice in said partial image.
Description
BACKGROUND OF THE INVENTION
[0001] 1. Field of the Invention
[0002] The present invention is directed to beam-hardening
correction in an X-ray computer tomography apparatus.
[0003] 2. Description of the Prior Art
[0004] In X-ray computed tomography, a shift of the average energy
of the X-rays toward higher values occurs as a consequence of the
polychromatic spectrum of the radiation emitted by the X-ray source
and as a consequence of the energy-dependent absorption of the
X-rays in the body of the patient under examination. This effect is
called beam hardening. This effect becomes more pronounced as the
transirradiated path in the body becomes longer. In the
reconstructed image of the transirradiated body slice, this
beam-hardening effect leads to unwanted image artifacts that
negatively affect the precise medical interpretation of the
image.
[0005] Standard algorithms (for instance, polynomial correction)
are known for the correction of such image artifacts caused by beam
hardening. These produce satisfactory results as long as the
spectral absorption or attenuation behavior of the transirradiated
body substances does not significantly differ from the spectral
attenuation behavior of a reference substance for which the
correction algorithm was developed. Water is used as the reference
substance in the standard case since water exhibits a spectral
attenuation behavior comparable to soft tissue in the human body
and the human body is largely composed of soft tissue.
Beam-hardening errors then can be eliminated to a significant
extent in body regions where essentially only soft tissue is
encountered. When, however, the X-rays also passes through bone
tissue, the algorithm is no longer accurate since bone tissue
exhibits a spectral attenuation behavior that deviates
substantially from water. The same is also true, for example, of
vessels filled with contrast agent. Since the extent to which soft
tissue and bone tissue were responsible for the beam attenuation is
initially unknown for the measured values acquired in the course of
the examination of a patient, a satisfactory beam hardening
correction is not possible based solely on knowledge of the
measured values.
[0006] Methods referred to as retrospective correction methods were
therefore developed wherein an overall image of the transirradiated
body slice is first reconstructed from the measured, overall
attenuation values, and this overall image is subsequently analyzed
and resolved into sub-images. Each of the sub-images shows only a
part of the various body substances. In the standard case, a bone
image and a soft tissue image are generated. Partial attenuation
values that indicate the beam attenuation by the appertaining part
of the body substances, i.e., for example, bone tissue or soft
tissue, are then calculated from the individual sub-images by
re-projection. Subsequently, correction values that are added to
the originally measured overall attenuation values are determined
for the partial attenuation values of each sub-image. For example,
the correction values are taken from correction characteristics
that were separately determined in advance for the respective body
substances on the basis of reference materials with comparable
attenuation. An overall image--which is now corrected for beam
hardening--of the transirradiated body slice is reconstructed a
second time from the corrected, overall attenuation values.
[0007] More detailed information about retrospective (post
construction) correction methods may be found, for example, in "A
Comparative Study of two Postreconstruction Beam Hardening
Correction Methods" by G. T. Herman, S. S. Trivedi, IEEE
Transactions on Medical Imaging, MI-2, 1983, pp. 128 ff., and in "A
Method for Correcting Bone Induced Artifacts in Computer Tomography
Scanners" by P. M. Joseph, R. D. Spital, Journal of Computer
Assisted Tomography, No. 2, 1978, pp. 100 ff.
[0008] It has been shown in practice that the known retrospective
correction methods can in fact clearly reduce image artifacts
caused by beam hardening compared to traditional, standard
algorithms, however, image artifacts continue to be observed and
elimination or at least reduction thereof is desirable.
SUMMARY OF THE INVENTION
[0009] An object of the present invention is to provide a computed
tomography apparatus with improved beam-hardening correction.
[0010] In a first version of the solution, this object is achieved
in an X-ray computed tomography apparatus constructed and operating
as follows.
[0011] A radiator/detector arrangement supplies a set of measured
intensity values for each X-ray projection of a body slice of a
patient under examination, each measured value thereof being
representative of the intensity of the X-rays that have passed
through the body slice in a respective partial projection region of
the overall projection region. An electronic evaluation and
reconstruction unit is connected to the radiator/detector
arrangement and is configured for
[0012] a) determining an overall attenuation value for each
measured intensity value, the overall attenuation value being
representative of the actual overall attenuation of the X-rays
produced in the body slice in the appertaining partial projection
region;
[0013] b) reconstructing an overall image of the body slice
proceeding from the overall attenuation values;
[0014] c) extracting a first partial image from this overall image
wherein essentially only those image parts of the overall image are
contained that correspond to a first part of the various substances
occurring in the body slice;
[0015] d) determining respective first attenuation partial values
allocated respectively to each overall attenuation value on the
basis of this first partial image, the first attenuation partial
value being a criterion for the attenuation that the X-rays
experiences in the respective projection partial region due to the
first part of the substances;
[0016] e) extracting a second partial image from the overall image
of the body slice wherein essentially only those image parts of the
overall image are contained that correspond to a second part of the
substances in the body slice differing from the first part;
[0017] f) determining respective, second attenuation partial values
on the basis of this second partial image allocated respectively to
each overall attenuation value, the second attenuation sub-value
being a criterion for the attenuation that the X-radiation
experiences in the respective projection partial region due to the
second part of the substances;
[0018] g) determining a correction value for every overall
attenuation value on the basis of previously determined
beam-hardening correction information stored in the evaluation and
reconstruction unit and dependent on the two attenuation partial
values; and
[0019] h) determining an overall attenuation value corrected for
beam hardening for each overall attenuation value according to the
following equation:
g.sub.corr=g-k(t.sub.1, t.sub.2) (1).
[0020] wherein g is the overall attenuation value, g.sub.corr is
the overall attenuation value corrected for beam hardening, t.sub.1
is the first attenuation partial value, t.sub.2 is the second
attenuation partial value and k(t.sub.1, t.sub.2) is the correction
value dependent on t.sub.1 and t.sub.2.
[0021] For determining the beam hardening correction information,
in accordance with the invention a set of reference overall
attenuation values g.sub.ref (s.sub.1, s.sub.2) is determined for a
material combination of a first reference material and a second
reference material different therefrom. This set of reference
overall attenuation values g.sub.ref (s.sub.1, s.sub.2) is
representative of the actual overall attenuation of the X-rays
produced by this material combination at various respective
thicknesses of the first material and the second reference
material. For this determination, s.sub.1 references a first
individual attenuation value that is representative of the
theoretical linear attenuation of the X-rays by the first reference
material for the respective thickness of the first reference
material, and s.sub.2 references a second individual attenuation
value that is representative of the theoretical linear attenuation
of the X-rays by the second reference material for the respective
thickness of the second reference material. The evaluation and
reconstruction unit determines (and uses) the aforementioned
correction according to the following equation:
k(t.sub.1, t.sub.2)=t.sub.1+t.sub.2-g.sub.ref(s.sub.1=t.sub.1,
s.sub.2=t.sub.2) (2).
[0022] In an alternative, second version, the inventive X-ray
computed tomography apparatus is constructed and operates as
follows:
[0023] A radiator/detector arrangement supplies a set of measured
intensity values for each X-ray projection of a body slice of a
patient under examination, each measured value thereof being
representative of the intensity of the X-rays that have passed
through the body slice in a respective partial projection region of
the overall projection region. An electronic evaluation and
reconstruction unit is connected to the radiator/detector
arrangement and is configured for
[0024] a) determining an overall attenuation value for each
measured intensity value, this overall attenuation value being
representative of the actual overall attenuation of the X-rays
produced in the body slice in the appertaining partial projection
region;
[0025] b) reconstructing an overall image of the body slice
proceeding from the overall attenuation values;
[0026] c) extracting a partial image from this overall image
wherein essentially only those image parts of the overall image are
contained that correspond to a first part of the various substances
occurring in the body slice;
[0027] d) determining respective attenuation partial values
allocated respectively to each overall attenuation value on the
basis of this partial image, the attenuation partial values being a
criterion for the attenuation that the X-rays experiences in the
respective projection partial region due to the first part of the
substances;
[0028] e) determining a correction value for every overall
attenuation value on the basis of previously determined
beam-hardening correction information stored in the evaluation and
reconstruction unit and dependent on the respective attenuation
sub-value; and
[0029] f) determining an overall attenuation value corrected for
beam hardening for each overall attenuation value according to the
following equation:
g.sub.corrg+k(t) (3),
[0030] wherein g is the overall attenuation value, g.sub.corr is
the overall attenuation value corrected for beam hardening, and
k(t) is the correction value dependent on t.
[0031] For determining the beam hardening correction information in
the second version of the invention, a set of reference overall
attenuation values g.sub.ref (s.sub.1, s.sub.2) is determined for a
material combination of a first reference material and a second
reference material different therefrom. This set of reference
overall attenuation values g.sub.ref (s.sub.1, s.sub.2) is
representative of the actual overall attenuation of the X-rays
produced by this material combination at various respective
thicknesses of the first material and the second reference
material. For this determination s, is a first individual
attenuation value that is representative of the theoretical linear
attenuation of the X-rays by the first reference material for the
respective thickness of the first reference material, and s.sub.2
references a second individual attenuation value that is
representative of the theoretical linear attenuation of the X-rays
by the second reference material for the respective thickness of
the second reference material. The evaluation and reconstruction
unit is configured for determining (and using) the overall
attenuation value dependent on the reference overall attenuation
values according to the following equation applies:
k(g, t)=t+s.sub.2-g.sub.ref(s.sub.1=t, s.sub.2) (4),
[0032] wherein
g.sub.ref(s.sub.1=t, s.sub.2)=g (5)
applies for g.sub.ref(s.sub.1=t, s.sub.2).
[0033] The two versions have in common the use of a correction
value that takes the attenuation by a combination of two different
materials into consideration. It has been shown in the human body
that the beam hardening by one substance (for instance, bone
tissue) is not independent of whether other substances (for
instance, soft tissue) are additionally present in the beam path.
However, the known retrospective correction methods are based
precisely on the premise that this precondition of independency
exits, by taking only the attenuation by a single (generalized)
substance into consideration. By employing a correction value
dependent on the attenuation of two materials, it is possible to
come very close to the actual conditions in the human body. Images
that are very low in disturbing image artifacts thus can be
generated, particularly given exposures of body regions having a
comparatively high proportion of bone.
[0034] Materials whose spectral attenuation behavior is similar to
the body substances that are to be taken into consideration in the
partial images are expediently selected as the reference materials.
For a partial image that should essentially show only soft tissue,
it is expedient to select water as reference material. For a
partial image that should essentially show only bone substance, for
example, a mixture of K.sub.2HPO.sub.4 and water can be selected as
reference material (S.C.E. Cann, Radiology 166, pp. 509-522
(1988)).
DESCRIPTION OF THE DRAWING
[0035] The single figure is a schematic illustration of a computed
tomography apparatus constructed and operating in accordance with
the principles of the present invention.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0036] The reference overall attenuation values for use in the
inventive computed tomography apparatus can be determined either by
computer simulation or by measurement. For the measurement, for
example, one can proceed such as shown in the figure. This shows a
CT scanner with an X-radiator 10 and a detector arrangement 12 that
is composed of a number of detector cells 14 arranged side-by-side
along a circular arc. The X-radiator 10 emits a fan-shaped X-ray
beam in a plane. The detector cells 14 cover an overall projection
region extending through the angular width of the beam fan, with
each individual detector cell 14 detecting the intensity of the
incident X-rays in the partial projection region it respectively
covers. Each cell 14 supplies a corresponding measured intensity
signal to an electronic evaluation and reconstruction unit 16. The
X-radiator 10 and the detector arrangement 12 can be moved in a
direction on normal to the fan plane without rotation along an axis
18.
[0037] Two wedges 20 and 22, respectively composed of different one
of the two reference materials, are situated in the beam path. The
wedges 20, 22 are arranged such that the thickness of the wedge 20
increases along the axis 18 and the thickness of the wedge 22
increases along the direction of the fan angle. When the X-radiator
10 and the detector arrangement 12 are displaced along the axis 18,
measured values are obtained for a number of different thickness
value pairs of the two reference materials. Using these measured
values, the evaluation and reconstruction unit 16 then calculates
the reference overall attenuation values. These indicate the actual
attenuation affected with beam hardening that the X-rays
experiences for the respective thicknesses of the two reference
materials. In order to compensate individual errors of the detector
cells 14, it is recommended to also scan the wedge 22 once with a
thickness gradient inverted along the fan angle direction, this
being indicated in broken lines at 22'.
[0038] After the reference overall attenuation values are
determined with the measuring structure according to the figure or
by simulation, one of the reference overall attenuation values
g.sub.ref (s.sub.1, s.sub.2) can be unambiguously allocated to each
pair of individual attenuation values s.sub.1 and s.sub.2
(potentially with the assistance of interpolations). The individual
attenuation values s.sub.1, s.sub.2 thereby respectively reference
the theoretical linear attenuation that the X-rays would experience
in case of energy-independent absorption in the first and second
reference material. They are linked with the thickness of the
material via the following relationship:
s.sub.1,2=d.sub.1,2.multidot..mu..sub.1,2 (6),
[0039] wherein d.sub.1,2 is the thickness of the first material or
the second reference material and .mu..sub.1,2 is an absorption
coefficient of the first or the second reference material that is
effective for linear attenuation.
[0040] Moreover, a reference attenuation error e.sub.ref (s.sub.1,
s.sub.2) can then also be unambiguously allocated to each pair of
individual attenuation values s.sub.1 and s.sub.2, this deriving
according to the following equation
e.sub.ref(s.sub.1, s.sub.2)=s.sub.1+s.sub.2-g.sub.ref(s.sub.1,
s.sub.2) (7)
[0041] from the difference between the sum of the individual
attenuation values s.sub.1 and s.sub.2 and the appertaining
reference overall attenuation value g.sub.ref (s.sub.1, s.sub.2).
This reference attenuation error e.sub.ref (s.sub.1, s.sub.2)
represents the beam hardening error by which the reference overall
attenuation value g.sub.ref (s.sub.1, s.sub.2) is lower than the
sum of the individual attenuation values s.sub.1 and s.sub.2 as a
consequence of beam hardening.
[0042] In an analogous way, the other individual attenuation value
s.sub.2 or s, can be unambiguously determined for each pair of a
reference overall attenuation value g.sub.ref (s.sub.1, s.sub.2)
and one of the individual attenuation values s.sub.1 and s.sub.2.
The appertaining reference attenuation error e.sub.ref (s.sub.1,
s.sub.2) then can also be unambiguously determined.
[0043] The above considerations are utilized in the invention in
order to find the respectively correct correction value during
operation of the CT scanner given examination of a patient. In the
first version of the invention, the two respectively identified
attenuation values t.sub.1 and t.sub.2 are employed as parameters
therefor; in the second version, one identified attenuation value t
and the overall attenuation value g are employed. When
s.sub.1=t.sub.1 and s.sub.2=t.sub.2 are set in the first version,
then an appertaining reference overall attenuation value g.sub.ref
(s.sub.1=t.sub.1, s.sub.2=t.sub.2) and thus an appertaining
reference attenuation error e.sub.ref (s.sub.1=t.sub.1,
s.sub.2=t.sub.2), thus can be immediately unambiguously determined.
The value of this reference attenuation error is then employed as
correction value k(t.sub.1, t.sub.2), i.e.
k(t.sub.1, t.sub.2)=e.sub.ref(s.sub.1=t.sub.1, s.sub.2=t.sub.2)
=t.sub.1+t.sub.2-g.sub.ref(s.sub.1=t.sub.1, s.sub.2=t.sub.2)
(8)
[0044] The comparable case applies given the second version of the
invention. When s1=t and g.sub.ref (s.sub.1=t, s.sub.2) are set
therein, an appertaining individual attenuation value s.sub.2, and
thus an appertaining reference attenuation error e.sub.ref
(g.sub.ref=g, s.sub.1=t), can be immediately unambiguously
determined. The value of this reference attenuation error is then
employed as correction value k(g, t), i.e
k(g, t)=e.sub.ref(g.sub.ref=g, s.sub.1=t)
=t=s.sub.2-g.sub.ref(s.sub.1=t, s.sub.2) (9).
[0045] One or more gray scale value thresholds according to which
the overall image is resolved into its various gray scale value
regions can, for example, be defined in order to extract the
partial images from the overall image. It has proven expedient when
one of the two partial images in the first version, or the single
partial image in the second version, essentially shows only bone
substance that is present in the transirradiated region. In the
first version, the correction value is then determined dependent on
the re-projected bone attenuation and a further attenuation partial
value acquired by re-projection, preferably of the soft tissue
attenuation; whereas, in the second solution, the correction value
is determined dependent on the re-projected bone attenuation and in
the overall attenuation value. The re-projected attenuation partial
values are preferably attenuation values that indicate the
theoretical linear attenuation in the respective body substance.
Details regarding how the attenuation partial values can be
determined from the partial images by re-projection can be derived,
for example, from the previously cited literature.
[0046] There are various possibilities regarding the concrete
implementation of the beam hardening correction information in the
inventive computed tomography apparatus. In the first version, the
identified reference overall attenuation values g.sub.ref(S.sub.1,
s.sub.2) can be stored in the form of a look-up table in a memory
of the evaluation and reconstruction unit 16 dependent on the
individual attenuation values s.sub.1 and s.sub.2. In this case,
the evaluation and reconstruction unit 16 would also execute the
arithmetic operation according to Equation (2) in order to obtain
the correction value. Instead of the reference overall attenuation
values, alternatively, the reference attenuation errors
e.sub.ref(s.sub.1, s.sub.2) can be directly stored in table form in
the evaluation and reconstruction unit 16 dependent on the
individual attenuation values s.sub.1 and s.sub.2.
[0047] In the second version, a look-up table can be stored in the
evaluation and reconstruction unit 16 that indicates the second
individual attenuation value s.sub.2 dependent on the first
individual attenuation value s.sub.1 and on the reference overall
attenuation value g.sub.ref (s.sub.1, s.sub.2). So that the
arithmetic operation according to Equation (4) need not be
constantly carried out by the evaluation and reconstruction unit
16, it is also possible to directly store the reference attenuation
errors e.sub.ref (s.sub.1, s.sub.2) in table form in the evaluation
and reconstruction unit 16 dependent on the reference overall
attenuation value g.sub.ref (s.sub.1, s.sub.2) and on the first
individual attenuation value s.sub.1.
[0048] In an optional embodiment of the first version, a function
u(x) that is dependent on a variable x can be determined for the
determination of the beam hardening correction information, this
function allocating a function value u(x) to every value of x,
with
x=A(Bs.sub.1+Cs.sub.2) (10)
[0049] this function value u(x) at least approximately corresponds
to the difference between the sum of the respective, two individual
attenuation values and the respective reference overall attenuation
value, whereby A, B and C are constants. The evaluation and
reconstruction unit 16 is configured for determining the correction
value according to the following equation:
k(t.sub.1, t.sub.2)=u(x=A(Bt.sub.1+Ct.sub.2)) (11)
[0050] The linear combination according to Equation (10) makes it
possible to reduce the dependency of the correction value
k(t.sub.1, t.sub.2) on two parameters to the dependency on one
parameter. The constants A, B and C are defined such that the error
between the reference attenuation error e.sub.ref (s.sub.1=t.sub.1,
s.sub.2=t.sub.2) and the function value u(x=A(Bt.sub.1+Ct.sub.2))
becomes optimally small.
[0051] In an optional embodiment of the second version,
analogously, a function v(y) dependent on a variable y can be
determined for the determination of the beam hardening correction
information, this function allocating a function value v(y) to each
value of y, with
y=D(Eg.sub.ref+Fs.sub.1) (12)
[0052] The function value v(y) at least approximately corresponds
to the difference between the sum of the respective, two individual
attenuation values and the respective reference overall attenuation
value, whereby D, E and F are constants. The evaluation and
reconstruction unit is configured for determining the correction
value according to the following equation:
k(g, t)=v(y=D(Eg+Ft)) (13)
[0053] The constants D, E and F are defined in this case such that
the error between the reference attenuation error e.sub.ref
(g.sub.ref=g,t.sub.1, s.sub.1=t) and the function value
v(y=D(Eg+ft)) becomes optimally small.
[0054] The two functions u(x), v(y) either can be implemented as a
look-up table in the evaluation and reconstruction unit 16 or in
the form of a mathematical algorithm, insofar as a suitable
approximation equation for the function u(x) or v(y) can be
found.
[0055] It is self-evident. moreover, that not only the calibration
measurements for the determination of the reference overall
attenuation values can be implemented at the CT scanner shown in
the figure, but also that the patient examination can ensue in the
scanner when, additionally, a rotation of the radiator 10 and the
detector arrangement 12 (insofar as this is not fashioned as ring
detector) is provided in the direction of the fan angle.
[0056] It should be noted that it is possible without further
difficulty to correct the overall attenuation values acquired in
the examination of a patient a priori with the assistance of a
standard algorithm, and to reconstruct the overall image from the
overall attenuation values corrected in this way. The
retrospectively determined correction values then will either be
added to the original, non-corrected overall attenuation values, or
the correction values will be reduced by the amount of the standard
correction.
[0057] Although modifications and changes may be suggested by those
skilled in the art, it is the intention of the inventors to embody
within the patent warranted hereon all changes and modifications as
reasonably and properly come within the scope of their contribution
to the art.
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