U.S. patent application number 11/933499 was filed with the patent office on 2009-08-13 for phase correction method.
Invention is credited to VLADIMIR JELLUS.
Application Number | 20090201021 11/933499 |
Document ID | / |
Family ID | 39420953 |
Filed Date | 2009-08-13 |
United States Patent
Application |
20090201021 |
Kind Code |
A1 |
JELLUS; VLADIMIR |
August 13, 2009 |
PHASE CORRECTION METHOD
Abstract
A method corrects for a phase error in an MR image, in which MR
signals of an examination subject are acquired, complex images of
the examination subject are generated, phase differences of the
phase values for various image points of the complex images are
established with an averaged phase value of image points from a
first surrounding region of a respective image point, and a phase
correction is executed dependent on how well the phase differences
correspond to a predetermined phase value, where the order of the
image points in which the phase correction is implemented is
dependent on how well the phase values in the image points
correspond to the predetermined phase value.
Inventors: |
JELLUS; VLADIMIR; (Erlangen,
DE) |
Correspondence
Address: |
SCHIFF HARDIN, LLP;PATENT DEPARTMENT
6600 SEARS TOWER
CHICAGO
IL
60606-6473
US
|
Family ID: |
39420953 |
Appl. No.: |
11/933499 |
Filed: |
November 1, 2007 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
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60856431 |
Nov 2, 2006 |
|
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Current U.S.
Class: |
324/309 |
Current CPC
Class: |
G01R 33/565 20130101;
G01R 33/56563 20130101; G01R 33/4828 20130101; G01R 33/5659
20130101 |
Class at
Publication: |
324/309 |
International
Class: |
G01V 3/00 20060101
G01V003/00 |
Claims
1. A method for correcting a phase error in an MR image,
comprising: acquiring MR signals of an examination subject;
generating complex images of the examination subject from the
acquired MR signals; establishing phase differences of phase values
for various image points of the complex images with, respectively,
an averaged phase value of image points from a first surrounding
region of a respective image point; executing a phase correction
dependent on how well the phase differences correspond to a
predetermined phase value, an order of the image points in which
the phase correction is implemented depends on how well the phase
values in the image points correspond to the predetermined phase
value; and providing a user readable or machine readable output
related to the phase correction.
2. The method according to claim 1, further comprising: utilizing
essentially only image points at which it as been checked how well
phase differences correspond to the predetermined phase value for
the calculation of the averaged phase value from the first
surrounding region.
3. The method according to claim 1, further comprising: checking
whether a formed phase difference of an image points lies within a
predetermined angular range with an averaged phase value from the
first surrounding region; and if yes, then leaving the phase value
of the checked image point unchanged; and if no, correcting the
phase value of the checked image point by a predetermined phase
value.
4. The method according to claim 1, wherein an order of the
establishment of the phase difference for the various image points
ensues dependent on how well phase differences of the individual
image points corresponding to the predetermined phase value, the
method further comprising: taking into account the corresponding
image point with the phase value in the phase correction in
proportion to a degree of correspondence of the phase difference of
an image point to the predetermined phase value.
5. The method according to claim 3, wherein the predetermined
angular range includes angles between 0.degree. and 90.degree., the
phase value being left unchanged if the phase difference is smaller
than 90.degree., while the phase value of an image point is
corrected by 180.degree. when the phase difference is greater than
90.degree..
6. The method according to claim 1, further comprising: determining
neighboring image points relative to image points for which the
phase difference should be established; determining, for the
neighboring image points, further phase differences of the
neighboring image points relative to an averaged phase value of
image points from a second surrounding region relative to the
respective neighboring image points; sorting the further phase
difference of the neighboring image points according to magnitude;
and selecting from the neighboring image points of a next image
point for which the phase correction is implemented, dependent on
the further phase difference.
7. The method according to claim 6, further comprising: sorting the
further phase differences of the neighboring image points into
stack ranges in which image points with phase values from a
predetermined phase range are situated; and processing stack ranges
with low phase ranges before stack ranges with higher phase
ranges.
8. The method according to claim 1, wherein the examination subject
comprises signal portions of at least two tissue types, the method
further comprising: identifying and separating the at least two
different tissue types.
9. The method according to claim 8, wherein the two tissues have a
different chemical shift and thus different resolution frequency,
the method further comprising: in the acquisition of the MR
signals, acquiring signals in which a phase position of the two
tissues is essentially identical in one case, and in an other case
acquiring signals in which phase positions of the two tissues are
aligned opposite to one another.
10. The method according to claim 8, further comprising: utilizing
two predetermined phase values that correspond to 0.degree. and
180.degree. as predetermined phase values; and checking whether the
determined phase differences correspond to 0.degree.
or180.degree..
11. The method according to claim 9, further comprising:
determining which tissue type is responsible for a resulting phase
value in an image point based on the MR signals in which the phase
positions of the two tissue types are opposite; and correcting the
phase value of an image point by 180.degree. or not depending on
the determined tissue type.
12. The method according to claim 11, further comprising: producing
a resultant phase curve that corresponds to system-dependent phase
error of the MR system in the phase values of the complex MR signal
after the identification of the two tissue types and the correction
of the phase difference by 180.degree. for one of the tissue
types.
13. The method according to claim 8, wherein the two different
tissue types are fat and water.
14. The method according to claim 1, wherein adjacent image points
from three different spatial directions are used for the averaged
phase value.
15. The method according to claim 1, wherein between three and nine
image points in each spatial direction are used for the averaged
phase values.
16. The method according to claim 16, wherein between six and eight
image points in each spatial direction are used for the averaged
phase values.
17. The method according to claim 15, wherein between five and
seven image points in each spatial direction are used for the
averaged phase values.
18. The method according to claim 1, further comprising: utilizing
a plurality of acquisition coils for the acquisition of the MR
signals; combining the complex MR signals of the individual coils
into a complex total signal before a phase correction is
implemented on the complex total signal.
19. The method according to claim 18, further comprising:
determining phase information of each acquisition coil; and taking
this phase information taken into account in calculating the
complex total signal.
20. The method according to claim 18, further comprising: assessing
a sensitivity of each acquisition coil before the formation of the
complex total signal; and in the formation of the total signal,
weighting a portion of the signal of each coil dependent on its
sensitivity.
21. The method according to claim 6, further comprising: taking
into account essentially only image points in which it has been
checked how well the phase differences correspond to the
predetermined phase value in the determining of the averaged phase
values of image points from the second surrounding region.
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] The present application claims the benefit of U.S.
Provisional Application No. 60/856,431, filed Nov. 2, 2006, herein
incorporated by reference.
BACKGROUND
[0002] The invention concerns a method for correction of a phase
error in an MR image. The invention can, for example, be used to
calculate the phase error that arises during the imaging due to
system instabilities or system imprecisions. Furthermore, the
invention can be used for splitting of signals from fatty tissues
from signals from aqueous tissues.
[0003] Imaging by way of nuclear magnetic resonance, i.e., magnetic
resonance tomography ("MR tomography") finds an ever wider field of
application in diagnostics. In addition to the innocuousness of the
radiated fields and in addition to the fact that the image plane
can be freely selected in MR tomography, an MR signal has the
advantage that the MR signal can be represented by complex numbers
and not just a scalar quantity as is, for example, the case given
conventional x-ray images or in computer tomography.
[0004] In an MR image, the magnitude of the MR signal and the phase
(i.e., the direction of the magnetization vector that corresponds
to the signal) exist for each image point. Given standard magnitude
imaging, the phase information is not used. However, there are also
applications for which the phase information is of greater
importance. For example, the phase information is used in order to
acquire information about the blood flow. The phase information
can, for example, also be used to depict the vessel structure or
for temperature imaging.
[0005] Given use of the phase information, in many applications,
the fundamental problem exists that not only does the desired phase
curve exist resulting from the radiated radio-frequency pulses (RF
pulses), but also includes other phase effects due to field
inhomogeneities or a temporal change of the external magnetic field
B0.
[0006] However, for many applications it is desirable to be able to
quantify the system-dependent phase errors in order to be able to
subsequently remove them when using the phase information in the MR
image.
[0007] One possible application field of phase-corrected MR images
lies, for example, in the splitting of the signals from two
different tissue components when the examined tissue comprises two
different components (e.g., fat and water). Given two different
tissues with a different chemical-related shift, a different
magnetic field results at the nucleus which leads to different
resonance frequencies. In the signal acquisition, this leads to
different phase angles of the two components. The most prominent
representatives of two different tissue types in the magnetic
resonance signal are fat and water, although other applications are
also possible. The resonance frequencies of fat and water differ by
approximately 3.5 ppm (parts per million). In many clinical MR
applications, it is desirable to suppress the signal of the fat
since the fat signal is typically very strong and, for example, can
occlude lesions.
[0008] A further application field of phase-corrected MR images
exists given pulse sequences with a previously inserted 180.degree.
inversion pulse, i.e., what are known as inversion recovery
acquisitions, or given other acquisitions in which a phase change
of 180.degree. can exist.
[0009] U.S. Patent Publication No. 2005/0165296 A1 describes a
phase correction method that is based on what is known as the
region growing algorithm, with which the system-dependent phase
error is calculated in that phase gradients within the MR image are
calculated and this phase gradient is used for a correction
algorithm in order to remove system-dependent phase errors.
However, two further phase images must be calculated for this
correction algorithm: a phase gradient image in the one direction
of the image plane as well as a phase gradient in the second
direction of the image plane, which makes the calculation
complicated.
SUMMARY
[0010] The present invention provides a method for phase correction
of phase errors that is very effective.
[0011] This object is achieved via a method for correcting a phase
error in an MR image, comprising: acquiring MR signals of an
examination subject; generating complex images of the examination
subject from the acquired MR signals; establishing phase
differences of phase values for various image points of the complex
images with, respectively, an averaged phase value of image points
from a first surrounding region of a respective image point;
executing a phase correction dependent on how well the phase
differences correspond to a predetermined phase value, an order of
the image points in which the phase correction is implemented
depends on how well the phase values in the image points correspond
to the predetermined phase value; and providing a user readable or
machine readable output related to the phase correction.
[0012] According to various embodiments of the present invention, a
method is provided for correction of a phase error in an MR image,
this method comprising the following steps: in one step of the
method, MR signals of an examination subject are acquired and
complex images are generated with the phase information of the
examination subject. In the phase correction method, phase
differences of the phase values for various image points of the
complex images are now calculated with a respective averaged phase
value of image points that originate from a first surrounding
region of a respective image point.
[0013] The calculation of the averaged phase value of the MR signal
can proceed as follows. Since the MR signal is a complex quantity
with real portion and imaginary portion, the sum of the signals of
the adjacent image points can be calculated in order to calculate
the averaged phase value, whereby the complex numbers are added in
the summation, which corresponds to a vector addition. The phase of
this sum is then compared with the phase of the examined image
point.
[0014] According to a different calculation type, an average value
of the sum of the phases can be calculated; in this example, each
image point equally contributes to the sum, even when an image
point comprises only noise. In the complex summation and the
subsequent comparison, the portions of the individual images points
are averaged dependent on the signal intensity since image points
with low signal also contribute only slightly to the sum given
complex addition. Also, no average value calculation is necessary
because the phase of the sum is equal to the phase of the average
value.
[0015] According to a further aspect of various embodiments of the
invention, the phase correction is implemented dependent on how
well the determined phase differences correspond to a predetermined
phase value. The order of the phase correction in the image points
is established in the implementation of the phase correction in the
various image points such that the order depends on how well the
phase values in the image points correspond to the predetermined
phase value. A reliable and fast-operating method is provided via
the establishment of the phase differences of an image point with
averaged phase value from a first surrounding region.
[0016] A stable, well-functioning method is achieved due to the
fact that the order of the image points when the phase correction
is implemented depends on how well the phase differences correspond
to a predetermined phase value. Given such correction methods in
which the image points are corrected bit by bit, and whereby the
results of preceding corrections are built upon, the "history" of
the correction method is important. Such methods are also known as
"region growing algorithms". A reliably-operating scheme for
correction of the phase error is achieved when image points that
exhibit a small phase error are used first, and the uncertain image
points (where it is uncertain whether the phase information is
correct) are preserved for a later point in time.
[0017] According to one embodiment of the invention, primarily only
image points at which the phase correction has been implemented,
i.e., at which it was checked how well the phase differences
correspond to the predetermined phase value, are taken into account
for the calculation of the averaged phase value from the first
surrounding region. Via the use of already phase-corrected image
points in the averaging of the phase values in the first
surrounding region, it is ensured that image points with possibly
false phase values are not taken into account for calculation.
[0018] The phase correction can, for example, be an examination as
to whether formed phase difference of the image points lies in a
predetermined angular range with the averaged phase value from the
first surrounding region. If this is the case, the phase value is
left unchanged. If the phase difference does not lie in the
predetermined angle range, for example, the phase value of the
examined image point can be corrected by a predetermined phase
value, meaning that the phase correction is implemented. In one
exemplary embodiment, the phase correction means that 180.degree.
is subtracted from the phase value. As is explained in more detail
below, the correction of the phase value with 180.degree. addresses
the fact that this phase value possibly concerns a different tissue
with a different phase value (such as, for example, fat). If
180.degree. is subtracted from the phase value, it is taken into
account that it is a different tissue (such as, for example, fat).
The remaining phase value then reflects, for example, the
system-dependent phase homogeneity that can subsequently be used in
order to identify the phase errors and remove these phase errors in
the further phase imaging.
[0019] The order of the establishment of the phase difference for
the various image points advantageously ensues dependent on how
well the phase differences of the individual image points
correspond to the neighboring image points of predetermined phase
values; the better that the phase difference of an image point
corresponds to the adjacent image points from a second environment
of the predetermined phase value, the more likely that the
corresponding image point with the phase value is taken into
account in the phase correction. The image points given which the
phase difference of 0.degree. or 180.degree. can be reliably
identified are used and accounted for first. When it is
subsequently assumed that the phase error varies only slowly and
not abruptly across the MR image, i.e., across the various image
points, this fact can be taken into account for phase
correction.
[0020] In a preferred embodiment, it is examined whether the phase
difference corresponds not to one but rather to two predetermined
phase values, namely 0.degree. and 180.degree.. In this application
case it, is checked whether the determined phase differences
correspond to 0.degree. or 180.degree.. The better that the phase
difference corresponds to 0.degree. or, respectively, 180.degree.,
the more likely that the image point is taken into account in the
phase correction. Given the check of whether the phase difference
of the image point lies in a predetermined angular range relative
to the image points from the first surrounding region, in one
embodiment it can be examined whether the phase difference lies
between 0.degree. and 90.degree. or between 90.degree. and
180.degree.. For example, if the angle lies between 0.degree. and
90.degree., it can be assumed that the ideal phase (i.e., of the
predetermined phase value) lies at 0.degree.. If the calculated
phase difference of the phase values with the average value of the
phases from the first surrounding region lies in a range of greater
than 90.degree., it can be concluded that the ideal, predetermined
phase value is 180.degree.. In this case 180.degree. is subtracted
from the phase value of the examined image point.
[0021] Such a correction by 180.degree. in particular occurs in the
two-point Dixon technique. In this two-point Dixon technique, MR
exposures are created in which an echo signal is generated once
given a sample of two tissues (such as water and fat), in which
both components (fat and water) have the same phase position, and
the signal adds both components. Furthermore, a different echo
point in time is selected at which the phase position of the one
tissue (such as water) is opposite the phase position of the of the
other tissue (such as fat).
[0022] The phase position for the image point at opposite phase
position (what is known as an "opposed phase image") now depends on
which components most strongly contribute to the signal. If a phase
position in proximity to 180.degree. is now detected and not a
phase of 0.degree. (as is the case of identically-positioned
phase), it can be assumed that (for example) the fat is the
dominating tissue portion. With a method so described, it can now
be determined at which image points fat is responsible for the
phase position and at which image points water is responsible. If
fat is responsible for the phase position, the phase position is
inverted by 180.degree. in order to obtain the corresponding phase
position of the water; or, expressed otherwise, in order to deduct
the influence of the phase due to the fat signal. Which tissue type
is present in which image point can thus be identified.
[0023] The formed phase difference can be corrected by 180.degree.
or not dependent on this knowledge of the tissue type. After this
correction of the phase change induced by the fatty tissue, a phase
curve in the phase values of the complex MR signal now remains that
corresponds to the system-dependent phase errors of the MR system
that arise in the time that lies between the signal acquisition of
the signals at which the phase position of both tissues are
parallel to one another and the point in time of the signal
acquisition at which the phase position of the two tissues was
opposite.
[0024] According to a further aspect of the invention, in the
correction method, the neighboring image points are determined
relative to the image points of which the phase difference should
be formed. For the neighboring image points, a further phase
difference of the respective neighboring image points is then
determined relative to averaged phase values of image points from a
second surrounding region of the neighboring image points;
already-corrected image points are likewise used for the averaged
phase values from the second environment. The further phase
differences of the neighboring image points are subsequently sorted
according to magnitude, and the next image points for which the
phase correction is implemented is selected from the neighboring
image points, whereby the selection ensues dependent on the further
phase difference.
[0025] The further phase differences of the neighboring image
points are advantageously sorted in the stack ranges. In these
stack ranges, the image points with their phase values are
organized with predetermined phase ranges. Stack ranges with
smaller phase ranges, i.e., phase values with a smaller angular
range, are hereby processed before stack ranges with larger phase
ranges.
[0026] In the individual stack ranges, an image point can be
processed according to a FIFO (First In First Out) principle,
meaning that the image points in a stack range are processed not
according to their magnitude, but rather dependent on their input
into the stack range. The stack ranges in total are processed
according to magnitude, meaning that stack ranges with small phase
values are processed before stack ranges with large phase
values.
[0027] According to a further aspect of the invention, phase values
of adjacent image points from three different spatial directions
can be used for the averaging. In the method that was used in the
previously described U.S. Patent Publication No. 2005/0165295 A1,
only phase gradients in the image plane are used. Points in the
third spatial direction are not used.
[0028] For the averaging of the phase values in each spatial
direction, between three and nine image points are used that are
adjacent to the image point for which the phase difference should
be calculated relative to the neighboring image points. For
example, image points from a 5.times.5 (2D case) or
5.times.5.times.5 (3D case) environment or a 7.times.7 or,
respectively, 7.times.7.times.7 environment can be used for the
sorting of the image points in the stack, whereby only checked
image points from this environment are taken into account. An
averaged phase value is necessary, on the one hand, for the
difference establishment relative to the individual image points of
the MR image (the phase value from the first surrounding region)
and an averaged phase value of the neighboring image points
relative to their neighboring image points, i.e., from a second
surrounding region is in turn necessary.
[0029] This second averaged phase value serves to arrange the
neighboring image points of the image point for which the phase
correction should be implemented dependent on the phase differences
in the stack. For example, 7.times.7.times.7 image points can be
used in the first averaging while 5.times.5.times.5 image points,
for example, can be used in the second averaging for sorting of the
neighboring image points in the stack. Naturally, equally many
image points can be used for both averagings, or more image points
can be used for the second averaging than for the first
averaging.
[0030] For the acquisition of the MR signals, in a further
application case, it is possible that a plurality of acquisition
coils are used in order to acquire the MR signals for image
reconstruction. These different complex MR signals from various
channels can advantageously be combined into a complex total signal
first before the phase correction is conducted on the complex total
signal. This has a number of advantages. A first advantage is that
the complex total signal has a much better signal-to-noise ratio
than the individual MR signals from the different coils. The
correction of the phase error method is more robust due to the
increased signal-to-noise ratio since fewer phase errors are
induced by the noise.
[0031] A further advantage exists in that the phase correction
method need only be implemented on a single image. For example, if
twelve different coils are used for signal acquisition, the phase
defects must be corrected for twelve different complex MR images.
Procedurally, this is a very elaborate method. The calculation and
phase correction are significantly accelerated via the use of a
single complex total signal.
[0032] To form a complex total signal, it can be advantageous to
determine the sensitivity and phase information of each acquisition
coil and to take these into account in the qualification of the
complex total signal. Each coil can have an influence on the phase
value in the MR signal. When this information is taken into account
before the addition to a complex total image, the complex total
image no longer comprises coil-induced phase information.
[0033] Furthermore, to form the complex total signal, it is
desirable to estimate the sensitivity of each coil, where the
proportion of each coil in the total signal is weighted dependent
on the sensitivity of each coil. For example, given signal
acquisitions, this has the advantage that coils that have a very
poor signal-to-noise ratio for an examination region contribute
less to the total signal than coils that have a much better
signal-to-noise ratio for this region. Via weighting of the
individual coils, the coils whose detected signal is better than
the signal of other coils whose proportion relative to the total
signal is less contribute more to the total signal.
[0034] In the method according to U.S. Patent Publication No.
2005/0165296 A1, the individual images were compared given use of a
plurality of coils. When the plurality of the individual images
(for example, for an image point) have phase values that allow it
to be concluded that these relate to an aqueous tissue while a
lower number of images support the presence of fatty tissue at this
image point, via a majority decision, it can be determined which
tissue is probably present at the image point. However, this
calculation is very computation- and time-intensive and
complicated. The signal-to-noise ratio is improved via the
formation of a complex total signal that is subsequently used for
the phase correction, which improves the correction method, and
furthermore the number of the data to be processed is significantly
reduced.
DESCRIPTION OF THE DRAWINGS
[0035] The various embodiments of the invention are subsequently
explained in detail with reference to the accompanying
drawings.
[0036] FIG. 1 is a flow chart of a phase correction method
according to an embodiment of the invention;
[0037] FIG. 2 is a further flow chart with the steps for correction
of a phase error according to an embodiment of the invention;
[0038] FIG. 3 is a schematic diagram illustrating the magnetization
of two different tissue types at two different echo points in
time;
[0039] FIG. 4 is a pictorial illustration of a section from an
image using which the phase correction method is explained;
[0040] FIG. 5 is a pictorial illustration of a stack with a
plurality of stack ranges in which the image points are organized
dependent on the phase difference;
[0041] FIGS. 6A, B is a flow chart of a phase correction method
according to an embodiment of the invention;
[0042] FIG. 7-19 are exemplarily pictorial representation showing a
use of the individual image points in a correction method; and
[0043] FIG. 20 is a flow chart of a further application case for
the phase correction method of an embodiment of the invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0044] Schematically presented in FIG. 1 is a flow chart which
shows the steps that can be used for an embodiment of the inventive
phase correction method. After the start of the method in step 10,
the MR signals are acquired by one or more acquisition coils in
step 11, where complex MR images with phase information are
generated in step 12.
[0045] In a further step 13 of the method, a phase difference of
the image points relative to an averaged phase value from a first
surrounding region is calculated. In step 14, it is then checked
whether the calculated phase difference coincides with a
predetermined phase value or, respectively, two predetermined phase
values. Dependent on the coincidence, a phase correction is
implemented or not implemented in step 15, and in step 16 it is
checked whether all image points are processed. In the event they
are, the method ends in step 17; in the event they are not, the
process returns to step 13.
[0046] It is subsequently explained in which context the method
from FIG. 1 can be employed. If an MR signal is acquired from a
tissue with two tissue components, such as fat and water, both
tissue components have a different resonance frequency. When two
echoes (such as, for example, gradient echoes) are now acquired,
these two echoes can be selected via the selection of the echo time
such that the phase position of the water coincides once with the
phase position of the fat, while in the second echo, the phase
position of the water is aligned opposite to the phase position of
the fat. After the signal processing and Fourier transformation,
two images result: an image with coinciding phase position and a
further image with opposite phase position (what is known as the
in-phase or, respectively, opposed-phase images). The signal in the
two images can be written as follows (while disregarding the tissue
relaxation):
S.sub.0(m,n)=(W+F)e.sup.i.PHI..sup.0 (1)
S.sub.1(m,n)=(W-F(e.sup.i(.PHI.0-.PHI.) (2)
[0047] The water portion and the fat portion in a given image point
are represented by W or, respectively, F, where m or, respectively,
n designates the location of the image point along the x-axis and
along the y-axis. Ideally the phase is zero at the echo point in
time. .PHI..sub.0 now indicates the phase in the image that results
due to field inhomogeneities and due to a static phase error that
can occur in the signal and acquisition chain. The phase .PHI.
represents a further phase error due to the field inhomogeneity
that results between the in-phase echo and opposed-phase echo.
[0048] When the phase errors are now identified and should be
removed, in a first step it must be established in which image
point the fat signal or, respectively, the water signal is the
dominating component since the phase information in each image
point depends on this fact. In order to now determine the fat and
water content in each image point, the two phases .PHI..sub.0 and
.PHI. must be eliminated. This can also occur in the following
manner:
S'.sub.0(m,n)=S.sub.0(m,n)e.sup.-i.PHI..sup.0=W+F (3)
S'.sub.1(m,n)=S.sub.1(m,n)e.sup.i.PHI..sup.0=(W-F)e.sup.-i.PHI.
(4)
[0049] e.sup.-i.PHI..sup.0 can be determined via the ratio of the
magnitude of the image S0 over the image itself, with
e.sup.-i.PHI..sup.0
e.sup.-i.PHI..sup.0=|S.sub.0(m,n)/S.sub.0(m,n) (5)
[0050] However, given magnetic field inhomogeneities, .PHI. is not
zero. As is to be recognized from equation (4), the phase .PHI. of
the magnetic field inhomogeneity depends on whether fat or water is
the dominating signal portion in the tissue.
[0051] The basis of the phase correction algorithm is subsequently
explained in connection with FIG. 3. In FIG. 3, the magnetization
of the water 17 and the magnetization of the fat 18 are shown on
the left side at an echo point in time at which they have the same
phase position. In this case, the two magnetizations are added.
When the magnetization of the water 17 is aligned opposite the
magnetization of the fat 18 in the right part of FIG. 3.
[0052] In the shown example, the magnetization vector of the water
is greater than that of the fat, such that the total magnetization
perceivable in the image points points in the direction of the
water. In what is known as the opposed-phase image format that is
shown to the right in FIG. 3, the total phase position that is
comprised in the image point now depends on whether the fat portion
or the water portion dominates. If the fat portion should dominate,
the magnetization 18 of the fat that is aligned counter to the
water magnetization would be the greater vector, such that in
total, the phase vector is aligned opposite to the example
presented to the left in FIG. 3.
[0053] In summary, this means that given a fat-dominated image
point the phase position in the opposed-phase image should ideally
by 180.degree. while it should otherwise be 0.degree.. Since the
quantity W-F from equation (4) can now be either positive or
negative dependent on whether the fat portion or the water portion
is dominant, equation (4) can be rewritten as follows:
e.sup.-i.PHI.=.+-.S'.sub.1(m,n)/|S'.sub.1(m,n)| (6)
[0054] If the phases should now be determined based on the phase
inhomogeneity in order to taken them into account in the phase
determination, it must first be identified in which image points
fat or, respectively, water is the dominant portion. In the event
that fat is the dominant signal portion, the phase value must be
corrected by 180.degree. in order to remove the phase influence of
the fat portion from the image. The phase correction method is now
based on the identifying the image portions with dominating fat
portion, accounting for the phase influence due to the fact and
removing it. The phase remaining after this phase correction
represents the phase error due to the laterally-variable field
inhomogeneity.
[0055] Ideally, the phase values thus amount to either 0.degree. or
180.degree. in the opposed-phase image. However, in reality, these
phase values fluctuate due to the field inhomogeneity that results
between the first echo and the second echo. In what is known as a
region growing method, the pixels can now be determined in which
probably fat or probably water is the dominating signal portion in
order to then subsequently correct the phase by 180.degree. in the
event that fat is the dominating signal portion.
[0056] When phase values between 10.degree. and 20.degree. occur in
an image point, it can be assumed with relatively large assurance
that it is a water signal component. Given phase values of
170.degree.-180.degree., it can likewise be assumed that these are
very probably fat signal portions in this image point. Given phase
values in proximity to 90.degree., however, this decision is more
difficult. In a subsequent example, it is now assumed that the
tissue component is probably water at this image point when phase
values of less than 90.degree. are present while the dominating
component is probably fat given values greater than 90.degree.. For
this examination, the phase value of each image point is compared
with an average value of the phase values from the first
environment and the phase value is then corrected or not.
[0057] In FIG. 2 illustrates how whether the dominating component
in the image point is fat or water can be determined with a phase
correction method which operates with effective reliability. The
method from FIG. 2 thereby employs the calculation of phase
differences of the examined image points relative to an averaged
phase value of adjacent image points. Given system-dependent phase
inhomogeneities, it can be assumed that the system-dependent phase
change changes only slightly or, respectively, slowly from image
point to image point over the image.
[0058] Only image points for which a phase correction was already
implemented are hereby taken into account in the averaging of the
phases of the neighboring image points. In order to design the
phase correction method in a robust and efficient manner, the image
points are processed in an order, and, in fact, such that image
points given which the phase values relatively surely suggest a fat
or water content are processed first, while image points with less
certain phase values are processed at a later point in time.
[0059] The method shown in FIG. 2 starts in step 20. In an initial
step 21, for example, a marking is set to 0 for all image points of
the acquired MR images. In the event that a phase correction was
implemented in the image point at a later point in time, this
marking is set to 1 in order to indicate that this image point was
already processed, and to prevent that this image point is
processed again. In step 22, an empty stack is generated as it is
shown, for example, in FIG. 5. The individual image points in this
stack are organized dependent on phase differences that are
explained in detail below.
[0060] This stack 50 shown in FIG. 5 comprises a plurality of stack
ranges 51. In these stack ranges, the individual image points can
be placed dependent on their phase differences. In the shown
exemplary embodiment, the stack ranges 51 are dimensioned such that
the stack range accommodates phase differences of approximately
10.degree.. In terms of magnitude, the phase differences can assume
values between 0.degree. and 90.degree. such that nine stack ranges
were used in the shown exemplary embodiment. The stack ranges can
also be dimensioned differently.
[0061] An arbitrary starting image point from the opposed-phase
image is selected in step 23. In step 24, an image point with the
smallest .DELTA..PHI. value is subsequently selected from a stack
range. This means that the phase differences is with relatively
high probability in the area of 0.degree. or, respectively,
180.degree.. In step 25 the nearest neighbors of the selected image
point are determined. The neighboring image points are placed in a
stack dependent on an averaged phase value of the image points from
the neighborhood to the neighboring image points to the selected
image point.
[0062] In step 26, the phase difference of the originally selected
image point is calculated relative to the averaged phase value of
the neighboring image point. If this calculated phase difference is
smaller than 90.degree., the phase value is left unchanged; if the
calculated phase change is greater than 90.degree., the phase value
is corrected by 180.degree. (step 27). After the phase correction
was implemented in step 27, the selected image point is removed
from the stack, the examined image point is marked as
phase-corrected (step 28). For example, this can mean that the
value .PHI. is set from 0 to 1 in the mask initialized in step
21.
[0063] In the present example, a phase correction means the
examination of the phase difference, and in the event that the
phase difference is smaller than 90.degree. the phase value remains
unchanged; given values greater than 90.degree., the phase is
corrected by 180.degree.. Given image points at which the phase
correction was implemented, this can mean that the phase was
possibly left unchanged. However, in each case the phase difference
was examined relative to the neighboring image points.
[0064] In step 29, it is now determined whether image points that
are not yet examined are contained in the stack. If image points
are contained in the stack 50, the method returns to step 25 and
the next image point with the smallest phase difference is selected
from the stack. In the event that the phase correction was
implemented for all image points, the method ends in step 30.
[0065] The phase correction method is described in closer detail in
connection with FIG. 4-6.
[0066] As shown in FIG. 6A, the method starts in step 60. The stack
50 shown in FIG. 5 is prepared in a next step 61. At the beginning
of the correction method, no image point has yet been corrected and
a starting image point is selected in step 62. This image point is
marked as visited and checked. For example, this image point is
marked with "C" for "checked" and with "v" for "visited". For this
image point, it cannot be established whether it is an image point
with water content or fat content.
[0067] However, in the present state, this is also not of
importance. If it is an image point with fat signals, the water
signal portions are phase-corrected in the subsequent correction
method. The decision of which tissue portions are fat or water can,
however, only be made at the conclusion of the method. For example,
as a starting image point, an image point in the middle of the
image can be selected, or an image point with the highest magnitude
signal, or other requirements for the starting image point can also
be posed.
[0068] In the section from the MR image 40 shown in FIG. 4, for
example, the image point designated with A is the starting image
point for the correction method. In a next step 63, the direct
neighbors of this image point A are selected. In the shown example
these are the image points B, C, D and E. In the event that this is
a three-dimensional data set, the adjacent image points in the
third spatial direction can be used.
[0069] However, in another exemplary embodiment, a plurality of
neighbors can also be used, for example, in the two-dimensional
case under consideration of the image points F and H, I and K,
which would mean eight image points as nearest neighbors in the
two-dimensional case or 26 image points in the three-dimensional
case. However, in the subsequent example it is assumed that only
the four nearest neighbors B, C, D and E were selected.
[0070] In the next step 64, the phase difference of each
neighboring image point relative to adjacent image points is
calculated for each neighboring image point, for example 5.times.5
image points of this neighbor that were already checked (i.e., have
been marked with "C"). The phase differences of the respective
neighboring image points relative to the starting image point A are
then placed in the stack 50. For example, if the phase difference
for the image point E relative to the image point A is 5.degree.,
image point R would thus be placed in the uppermost stack range 51.
If the phase difference of pixel C relative to pixel A is
24.degree., pixel C would be placed in the third-uppermost stack
range etc. The neighboring image points are thus placed in the
stack based on their phase differences. The visited neighbors are
marked as visited. The neighbors are organized in stack ranges 51
in the stack shown in FIG. 5. For example, the stack range 51
comprises the phase difference values from 0 to 10.degree., a
second region comprises the phase differences from 11 to
20.degree., etc.
[0071] Every single stack range can hereby operate according to the
first-in, first-out principle. In total the stack, ranges are
processed according to magnitude, meaning that the stack range 0 to
10.degree. is processed before the stack range 11 to 20.degree..
However, in the stack range itself, processing can ensue according
to the first-in, first-out principle, meaning that the image points
in a stack range are processed dependent on their input into the
stack range.
[0072] In the next step 65, the next image point is then selected
from the stack, whereby the process begins with the still-full
stack range with the lowest phase values. In the phase difference
calculation, the phase difference is calculated between the complex
values of the neighboring image points and the examined image
point. This can lie between -180.degree. and 180.degree.. The
absolute value of this is now taken, meaning that the phase
difference now lies between 0 and 180.degree.. The stack range with
values between 0 and 10.degree. now exhibits phase differences
between 0 and 10.degree. and 170 and 180.degree., the second stack
range with values from 11 to 200 comprises these values and values
between 160 and 170.degree. etc. Considered otherwise, this means
that values between 0 and 180.degree. are present after taking the
absolute values.
[0073] When the phase difference is smaller than 90.degree., it
remains unchanged; given phase differences greater than 90.degree.,
the value is corrected by 180.degree.. The result of this
conversion is values between 0 and 90.degree., whereby the stack
ranges can in turn be arranged with stack ranges from 0 to
10.degree., 11 to 20.degree. etc. based on this result. It is
subsequently assumed that this is the image point E. The nearest
neighbors that were not yet marked as visited (i.e., here the image
points F, G and H) are visited in turn (step 66).
[0074] In the next step 67, the neighboring image points are placed
in the stack. As in step 64, an averaged phase value of the
surrounding pixels is calculated in turn and this averaged phase
value is compared with the phase value of the neighboring image
point for this placement of the neighboring image points in the
stack. Given the calculation of the averaged phase value, again,
only image points that have already been checked are taken into
account.
[0075] After the neighboring image points have been organized in
the stack, the phase difference is calculated for the image point
(which was selected in step 65) relative to an average value of the
phase values of the adjacent image points, whereby again only image
points that have already been checked (i.e., have been marked with
"C") are taken into account in the calculation. With regard to the
image point selected in step 65, for example, these neighboring
image points can be selected from a region of 7.times.7 or
7.times.7.times.7 image points around the selected image point.
Since only already-checked image points are used, this is the
starting image point A in the present example.
[0076] This means that the phase difference between the image
points A and E is calculated in step 68. In step 69, it is hereby
checked whether the calculated phase difference is smaller than
90.degree.. If this is the case, the phase value is left unchanged
for image point E. When the phase difference of E relative to the
examined neighbors (i.e., image point A) is greater than
90.degree., the calculated phase value of E is corrected by
180.degree. (step 70) since, in this case, it is assumed that in
this image point the fat signal is the dominating tissue. Via this
correction the phase, influence due to the fat is accounted for and
removed.
[0077] In step 71, this pixel E is then marked as checked, meaning
marked with "C" in the prior example and removed from the stack. In
step 72 the next image point from the stack 50 that lies in the
lowest stack range is subsequently selected. In step 73, the
neighboring image points that were not yet marked as visited are
again selected and visited as in step 66. In step 74, a further
phase difference is determined for each neighboring image point
relative to the averaged phase value of image points from a second
surrounding region.
[0078] This means that the method does not proceed as at the
beginning, since no neighboring image points have yet been checked;
the phase difference between selected image points and the
neighboring image points has not yet been calculated. Rather, the
phase difference of the neighboring image points and the sum of the
image points are determined in a second surrounding region. Again
only already-checked image points are hereby taken into account. In
the present case, these are two image points, namely the starting
image point A and the image point E that was checked subsequently
and that are taken into account for the averaging of the image
points adjacent to E.
[0079] The neighboring image points (relative to E) are again
sorted in the stack 50 in step 75 based on the phase difference of
the individual neighboring image points relative to their second
surrounding region. Given the closest neighbors in the
two-dimensional case, this means that four image points are
organized in the stack in step 75; in the three-dimensional case,
these are six image points. After the sorting of the image
processing system in the stack 50, that phase difference of the
image point relative to an average value of the phase values from
the first environment is now calculated for the image point for
which the neighbors were previously selected (namely for E).
[0080] For example, 7.times.7 image points in the two-dimensional
case or 7.times.7.times.7 image points in the three-dimensional
case can be used for this calculation. Again, only the
already-checked image points are used. In the present cases, these
are still the two pixels A and E (step 76). This calculated phase
difference is examined in step 77, meaning that it is established
whether it is smaller than 90.degree.. If it is greater than
90.degree., the phase value of the examined image point is again
corrected by 180.degree. in step 78. In the event that the phase
difference is smaller than 90.degree., the phase value is left
unchanged. In step 79, the checked image point is finally marked as
checked, meaning that the image point is marked with "C" in order
to signal that the phase was already checked at this image
point.
[0081] In step 76, the phase difference of the selected image point
is calculated relative to the already-marked image points from the
first environment. This difference establishment serves as a basis
for the phase correction in steps 77 and 78. In step 74, the phase
difference was likewise calculated relative to an average value of
the phase values of neighboring image points. This phase difference
establishment for each neighboring image point served for
organization of the image points in the stack. The stack controls
the progression of the phase correction. According to one aspect of
the invention, phase values at which the determined phase value
corresponds relatively well to the predetermined value 0.degree. or
180.degree. are considered first. If the phase value (i.e., the
phase difference relative to image points in the environment) lies
in proximity to 90.degree., the calculation is shifted to a later
point in time. The correction method is more stable due to the fact
that only already-checked and phase-corrected image points are
taken into account in the averaging.
[0082] After the marking of the image point as phase-corrected or,
respectively, checked in step 79, in step 80, it is checked whether
the stack (i.e., all stack ranges 51) are empty, that is, whether
all image points have been checked. If this is not the case, the
method reverts to step 72, in which the next image point in the
same stack range or from the next stack range is selected when the
previous stack range is empty.
[0083] The selection of the nearest neighbors relative to the
presently selected image point, the establishment of the phase
difference of the nearest neighbors relative to their second
environment, the sorting of the nearest neighbors into a stack
using the phase difference, and the calculation of the phase
difference for the image point that has been selected as a next
stack subsequently follow again. In the first pass, only two image
points from the surrounding image points have already been checked.
In this next pass, the number of the checked neighboring image
points that can be taken into account for the summation and
averaging of the neighboring image points increases to three. In
this manner the number of checked image points rises in each pass,
and also the possible number of image points that lie in the
surroundings and can be used for the averaging. How many image
points precisely can be used from the surroundings depends on,
among other things, the trajectory that results via the selection
of the next image point from the stack 50. If all image points are
checked in a last step, the stack 50 is emptied and the method ends
in step 81.
[0084] After the end of the step 81, the phase influence (for
example, due to the fatty tissue) is now corrected; the remaining
phase influence represents the phase inhomogeneity that results due
to system imprecisions. These phase errors can now be identified
and the phase errors can be removed in imaging methods. In the
event that the MR data were detected with a plurality of
acquisition coils, the individual complex MR images can first be
merged into a complex total image under consideration of the phase
of the individual coils.
[0085] Furthermore, the sensitivity of each coil can hereby be
taken into account. The sensitivity of each coil can, for example,
be calculated via an auto-correlation method in which the
eigenvector is calculated for the largest eigenvalue. The values of
the eigenvectors respectively yield the sensitivity. This can be
determined in advance. If the phase influence of each coil and the
sensitivity of each coil is now determined, the total signal can be
calculated via the weighting of the signals of the individual
components. A signal portion with good signal reception and high
signal level can hereby receive a higher weighting factor than a
signal portion with very low reception level and low
signal-to-noise ratio.
[0086] The use of this method, known as an adaptive combine method,
improves the signal-to-noise ratio overall since the complex total
image has a better signal-to-noise ratio than the individual
images. This improves the phase correction workflow. Furthermore,
the phase development of each coil is taken into account, which in
turn makes the method more robust and reliable. A further advantage
is the reduced data processing quantity, since only one image must
be phase-corrected and not various images for various channels.
[0087] For better understanding of the operation, the phase
correction algorithm illustrated in FIGS. 6A and 6B is explained
using exemplary images in FIGS. 7-18. Shown in FIG. 7 are image
points of a phase image that are designated with A-Q in the columns
and from 0-13 in the rows. At the beginning, a starting image point
is selected, analogous to step 62. In the illustrated case, this is
the image point with the coordinates I6. This starting image point
is marked as checked and visited, i.e., with "C" for checked and
"v" for visited.
[0088] As recognized from FIG. 8, after selection of the direct
neighboring image points (analogous to step 63), the neighboring
image point is visited, here image point I5. An environment of
5.times.5 image points is subsequently marked (shown in dashed
lines) for the image point I5. An averaged phase value is formed
for these image points within the dashed quadrilateral, whereby
only already-checked image points are considered, meaning image
points that are marked with C. In this case this is only the image
point I6. Image point I5 is placed in the stack on the basis of the
phase difference between the averaged phase value formed from I6
and the phase value of image point I5. I5 is likewise marked as
visited.
[0089] As is to be recognized in FIG. 9, if the same procedure that
was implemented for image point I5 is implemented for image point
H6, an averaged phase value of image points from the surroundings
is calculated under consideration of image points already checked
in terms of phase; this image point is placed in the stack
dependent on the calculated phase difference. In FIG. 10, it is now
to be recognized that all four direct neighbors of the image point
I6 have been visited and have been sorted in the stack.
[0090] In FIG. 11, it is shown how (analogous to step 65) the image
point from the stack with the least phase difference is selected.
In the shown example, this is the framed image point H6. As
mentioned in step 66 and shown in FIG. 12, the direct neighbors
that were not yet selected are selected again, i.e., the image
points G6, H5 and H7. These neighboring image points (that were
newly indicated with "v") are in turn sorted into the stack, as was
described in connection with FIG. 7-10. As is to be recognized in
FIG. 13, a first environment (in the shown case, image points in a
7.times.7 environment that are shown with a dash-dot line) is now
selected for the image point H6 taken from the stack.
[0091] A phase difference between the image point H6 and the
adjacent image points that were already checked (this is only the
image point I6) is hereby calculated (analogous to step 68). Due to
the phase difference between the selected image point H6 and the
averaged phase value from the surroundings, it is now checked
whether the phase difference is smaller than 90.degree. or not. The
steps follow analogous to steps 69-71, whereby after the check the
image point H6 is likewise marked as checked via marking with "C"
for "checked".
[0092] The image point H6 is subsequently removed from the stack
and the next image point with the smallest phase difference (image
point I5 in the example shown in FIG. 14) is taken from the stack.
For image point I5, the nearest neighbors are again visited, in
FIG. 15 the image point I4. The difference of the neighbors that
were already checked is calculated again for this image point. Two
image points (namely the image points H6 and I6) that are marked as
checked are taken into account in the averaging according to FIG.
15. After all neighbors of the image point I5 have been visited,
namely the image points I4, H5 and J5, the phase difference for
image point I5 relative to an averaged phase difference of the
surrounding image points (again selected from the dash-dot region)
is calculated as shown in FIG. 16. The two image points that are
marked with "C" are again taken into account in this calculation of
the surrounding image points. It is subsequently checked whether
the phase difference is smaller than 90.degree. or not and, in the
event that it is necessary, the phase value is corrected by
180.degree.; the image point I5 is also subsequently marked as
checked.
[0093] It is again to be recognized in FIG. 17 that image point I7
is used as a next image point from the stack, whereby in FIG. 18,
the nearest neighbors that were not yet visited are again selected,
i.e., the image points H7, I8 and J7. After averaging for these
individual neighboring image points with their respective
surroundings, as shown in FIG. 19, an environment of 7.times.7
pixels is again selected for the previously selected image point
(here image point I7) and a phase difference of this image point
with the averaged phase value of the adjacent image points that are
already corrected is calculated, in the present case under
consideration of three image points.
[0094] As can be learned in FIG. 6B, this correction algorithm runs
in a loop, whereby the number of already-checked image points is
small at the beginning of the correction and then grows slowly.
Quadratic surroundings are used as neighboring image points in
FIGS. 7-19; however, other surrounding regions and shapes (such as
circles etc.) can also be used. As is again clear from FIGS. 7-19,
only image points that were already checked (i.e., at which the
phase value was corrected by 180.degree. in the event that this was
necessary) are considered in the averaging in the surroundings. In
the method described here, the sorting of the image points (when
they are considered) ensues as part of the region growing method,
since here only checked image points are taken into account.
[0095] A further application case of the method is shown in FIG.
20. After the acquisition of the MR images and the removal of the
general phase .PHI.0 in step 81, a start image point can be
selected in step 82 and the region growing algorithm described in
connection with FIG. 6 is executed in step 83. After smoothing of a
phase in step 84, the image points with signal portion "fat" can
now be separated from the image points with signal portion "water"
in step 85.
[0096] In summary, the present invention enables a reliably
functioning method for correction of a phase error that can be used
in many different applications N in which the calculation with
correct phase values or, respectively, the removal of phase errors
is of importance.
[0097] For the purposes of promoting an understanding of the
principles of the invention, reference has been made to the
preferred embodiments illustrated in the drawings, and specific
language has been used to describe these embodiments. However, no
limitation of the scope of the invention is intended by this
specific language, and the invention should be construed to
encompass all embodiments that would normally occur to one of
ordinary skill in the art.
[0098] The present invention may be described in terms of
functional block components and various processing steps. Such
functional blocks may be realized by any number of hardware and/or
software components configured to perform the specified functions.
For example, the present invention may employ various integrated
circuit components, e.g., memory elements, processing elements,
logic elements, look-up tables, and the like, which may carry out a
variety of functions under the control of one or more
microprocessors or other control devices. Similarly, where the
elements of the present invention are implemented using software
programming or software elements the invention may be implemented
with any programming or scripting language such as C, C++, Java,
assembler, or the like, with the various algorithms being
implemented with any combination of data structures, objects,
processes, routines or other programming elements. Furthermore, the
present invention could employ any number of conventional
techniques for electronics configuration, signal processing and/or
control, data processing and the like. The word mechanism is used
broadly and is not limited to mechanical or physical embodiments,
but can include software routines in conjunction with processors,
etc.
[0099] The particular implementations shown and described herein
are illustrative examples of the invention and are not intended to
otherwise limit the scope of the invention in any way. For the sake
of brevity, conventional electronics, control systems, software
development and other functional aspects of the systems (and
components of the individual operating components of the systems)
may not be described in detail. Furthermore, the connecting lines,
or connectors shown in the various figures presented are intended
to represent exemplary functional relationships and/or physical or
logical couplings between the various elements. It should be noted
that many alternative or additional functional relationships,
physical connections or logical connections may be present in a
practical device. Moreover, no item or component is essential to
the practice of the invention unless the element is specifically
described as "essential" or "critical". Numerous modifications and
adaptations will be readily apparent to those skilled in this art
without departing from the spirit and scope of the present
invention.
* * * * *