USRE36679E - Method of cancelling ghosts from NMR images - Google Patents
Method of cancelling ghosts from NMR images Download PDFInfo
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- USRE36679E USRE36679E US08/198,866 US19886694A USRE36679E US RE36679 E USRE36679 E US RE36679E US 19886694 A US19886694 A US 19886694A US RE36679 E USRE36679 E US RE36679E
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R33/00—Arrangements or instruments for measuring magnetic variables
- G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
- G01R33/44—Arrangements or instruments for measuring magnetic variables involving magnetic resonance using nuclear magnetic resonance [NMR]
- G01R33/48—NMR imaging systems
- G01R33/54—Signal processing systems, e.g. using pulse sequences ; Generation or control of pulse sequences; Operator console
- G01R33/56—Image enhancement or correction, e.g. subtraction or averaging techniques, e.g. improvement of signal-to-noise ratio and resolution
- G01R33/565—Correction of image distortions, e.g. due to magnetic field inhomogeneities
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R33/00—Arrangements or instruments for measuring magnetic variables
- G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
- G01R33/44—Arrangements or instruments for measuring magnetic variables involving magnetic resonance using nuclear magnetic resonance [NMR]
- G01R33/48—NMR imaging systems
- G01R33/54—Signal processing systems, e.g. using pulse sequences ; Generation or control of pulse sequences; Operator console
- G01R33/56—Image enhancement or correction, e.g. subtraction or averaging techniques, e.g. improvement of signal-to-noise ratio and resolution
- G01R33/565—Correction of image distortions, e.g. due to magnetic field inhomogeneities
- G01R33/56563—Correction of image distortions, e.g. due to magnetic field inhomogeneities caused by a distortion of the main magnetic field B0, e.g. temporal variation of the magnitude or spatial inhomogeneity of B0
Definitions
- the present invention relates to a method for improving reconstructed NMR images and, more specifically, to a method for cancelling ghosts from NMR images.
- the objective can be stated as estimation of the true object density distribution x(n 1 ,n 2 ) from the observed ghosted image Y(n 1 ,n 2 ).
- experimental values of ⁇ (n 1 ,n 2 ) and ⁇ (n 1 ,n 2 +N/2) can be used to determine A(n 1 ,n 2 ) and B(n 1 ,n 2 ) by solving the above linear system of equations. Once A and B are determined, their magnitudes can be used to find x(n 1 ,n 2 ) and (n 1 ,n 2 +N/2) respectively.
- phase difference function is a function of the parameters for the NMR experiments. Some of these parameters are the strength of the x, y and z gradients, and the static magnetic field or the RF. Therefore, to be able to apply this method successfully, a different look up table is needed for different experimental set ups.
- the second drawback has to do with the fact that the phase difference function ⁇ (n 1 ,n 2 ) is somewhat object dependent. More specifically, although the general shape of ⁇ (n 1 ,n 2 ) does not vary drastically from one object to the next, the change is large enough to introduce considerable amount of ghosts.
- the third drawback of the above approach has to do with the fact that obtaining the phase difference function ⁇ (n 1 ,n 2 ) of a test object for all values of n 1 and n 2 is a non-trivial task from an experimental point of view. This has to do with factors such as susceptibility effects.
- the object of the present invention is therefore to provide a method for automatically eliminating ghosts in NMR signals resulting from the difference between even and odd line delays in a traversal of k-space using a sinusoidal readout gradient without using a look-up table.
- the present invention achieves the foregoing objective by a method involving the steps of:
- FIG. 1 shows a flow diagram of the ghost correction method of the present invention
- FIG. 2 depicts a reconstructed image with ghosts.
- FIG. 3 graphically depicts the phase difference function
- FIGS. 4a-11b show before/after examples of NMR images processed with the algorithm of the present invention.
- FIG. 1 a simplified block diagram of the method of the invention is shown.
- the raw NMR signal is converted to an image by performing a two dimensional inverse Fast Fourier Transform (FFT) 2.
- FFT Fast Fourier Transform
- the resultant image has ghosts, which are eliminated by processing the image with the ghost elimination algorithm 4 of the present invention.
- FIG. 2 depicts an image with ghosts. As shown therein, a bright line 6 represents the true image, while a less bright line 8 is a ghost of true image 6. Assuming that the traversal through k-space involves the sampling of 128 lines, the ghost will be separated by the true image by 64 lines, i.e. half the image size.
- FIG. 3 graphically depicts the phase difference function ⁇ (n 1 ,n 2 ).
- the phase difference function is appropriately symmetrical along the center of the n 2 axis.
- the phase difference function is defined by the offset ⁇ and slope ⁇ of a straight line 10 obtained by taking the least square estimation of a number of points; certain points 12,14 are eliminated (ignored) as being out-of-range since ⁇ (n 1 ,n 2 ) is assumed to vary smoothly.
- the ghost correction algorithm of the present invention takes advantage of the approximate shape of the phase difference function, which as described above, can be obtained experimentally for test objects.
- variation of the function ⁇ (n 1 ,n 2 ) is considerably smaller along n 2 than n 1 .
- Equation (12) Use ⁇ (n 1 ) and ⁇ (n 1 ) in equation (12) to find A(n 1 ,n 2 ) and B(n 1 ,n 2 ) for 0 ⁇ n 2 ⁇ N. From equations (9) and (10), the true object density distribution at (n 1 ,n 2 ) and (n 1 ,n 2 +N/2) are found by taking magnitude of A(n 1 ,n 2 ) and B(n 1 ,n 2 ), respectively.
- the program takes an input file representing the sampled time data or its two-dimensional (2-D) inverse Fourier transform, and generates an output file containing either the binary or hexadecimal version of the ghost-free image.
- the parameters used by the program are set by the operator in such a way that the performance of the algorithm is optimized. Some of these parameters such as "-g", “-c”, and “-f” are only used as switches to set flags, while others are used to set internal variables (either integer or floating point) to specific values.
- An example of the usage of the program is as follows:
- step 1. through step 3. of the algorithm is as follows:
- the "-g” flag determines whether or not the input ASCII file is the raw time data or its 2-D inverse Fourier transform. Specifically, if the "-g" option is set, then the program assumes the input file to contain raw time data, and computes the 2-D inverse Fourer transform of the data by successive application of the "ifft05" subroutine. This subroutine takes inverse FFT of one-dimensional sequences, and its listing is included in Appendix (B).
- the "-s” option sets the internal double precision variable "snr" used in steps 2. and 3. above.
- a large number of the columns in the ghosted input image correspond to empty space in the magnet, and therefore have no signal component.
- the signal energy for each column of the ghosted image is computed and compare it to a fixed threshold.
- This fixed threshold is the "snr" variable which is set by the "-a” option.
- the signal energy for the n 1 th column is defined to be: ##EQU10## where Y(n 1 ,n 2 ) denotes the value of the ghosted image at location (n 1 ,n 2 ).
- the AGC algorithm only processes columns whose energies exceed the threshold set by the variable "snr".
- An appropriate value of "snr” is 5 for input files containing raw time data, and 2 ⁇ 10 8 for the ones containing the 2-D inverse Fourier transform of the raw time data.
- Step 4. of the algorithm is now described in more detail.
- the phase difference function ⁇ (n 1 ,n 2 ) can be found experimentally by placing a test object in the lower or upper half of the FOV. Specifically, the ghost of a test object at location (n 1 ,n 2 ) with ##EQU11## appears at (n 1 ,n 2 +N/2), and vice versa.
- the location of the ghost of a pixel at (n 1 ,n 2 ) is (n 1 ,(n 2 +N/2) mod N).
- an object only fills out half of the FOV, its ghost does not overlap with itself in the reconstructed image.
- phase difference function associated with the object and the particular experimental set up can be determined empirically for regions of the reconstructed image which correspond to the object rather than its ghost.
- these cases correspond to the object being in the lower or upper half of the FOV.
- phase difference function can only be determined for pixels whose ghosts are not superimposed on pixels corresponding to other parts of the object. This information about ⁇ (n 1 ,n 2 ) can be exploited to find the parameters ⁇ and ⁇ as defined by equation (12).
- Pixels which correspond to bright (high intensity) parts whose locations correspond to either empty space in the FOV or parts of the object with very little or no energy will be referred to as "ghosting pixels". Specifically, if the pixel at location (n 1 ,n 2 ) is a ghosting one, then by definition:
- the pixel at location (n 1 ,(n 2 +N/2) mod N) corresponds to a low energy part of an object or empty space in the FOV. That is
- Step 4 of the automatic ghost correction algorithm derives the parameters associated with the n 1 th column in two steps. Specifically, it first finds the value of the phase difference function for all the "ghosting pixels" of the column, and then solves an overdetermined linear system of equations to find linear least square estimates of ⁇ (n 1 ) and ⁇ (n 1 ). At this point, the key question which remains to be answered is the way ghosting pixels are detected.
- the present invention uses two criteria for classifying pixels as ghosting ones.
- the first criterion is a direct consequence of equation (11) and the second part of the definition of ghosting pixels. It takes advantage of the fact that the magnitude of the even and parts of a ghosting pixel at location (n 1 ,n 2 ) are identical. Specifically, if Y(n 1 ,n 2 ) is a ghosting pixel, from equation (11):
- the appropriate values of "eoratio” is anywhere between 1 and 2.
- the "-r” option (the internal variable “eoratio") is set to 1.5. If it is set to small values (i.e. too close to 1), then the number of ghosting pixels will be too small, and therefore estimation of ⁇ (n 1 ) and ⁇ (n 1 ) will not be robust. On the other hand, if it is set to larger values such as 2 or even 3, then the chosen pixels might not necessarily be the ghosting ones. This will increase the error in the observations for the linear least-squares estimation, and therefore will result in less accurate estimation of ⁇ (n 1 ) and ⁇ (n 1 ).
- the magnitude of x(n 1 ,n 2 ) must be large (i.e. not at the noise level) and the magnitude of x(n 1 ,n 2 +N/2) must be very small (i.e. not at the noise level).
- this threshold is column dependent and becomes larger as the indices of the column become closer to N s /2.
- the threshold for the n 1 th column is:
- the "-t” option (the internal double precision "threshold”) is set to 100.
- the appropriate value for the "-t” option depends on the amount of ghosting in the central part of the image, and lies between 1 and 10000. If the reconstructed image suffers from considerable amount of ghosting in the central columns, then "threshold" must be set at a small value e.g. 1. Otherwise, it should be set at a larger value, say 100, so that the center 30 columns of the image remain more or less unchanged by the algorithm. If the central columns of an image are ghost-free, setting the "-t” option at small values might result in unnecessary distortions in these columns.
- the first ghost detection criterion checks the ratio between the magnitudes of even and odd parts of the pixel at location (n 1 ,n 2 ). If this ratio is close to one, then either Y(n 1 ,n 2 ) or Y(n 1 ,n 2 +N/2) are classified as ghosting pixels. To resolve this ambiguity and to improve the detection procedure, a second criterion is used which computes the ratio shown in equation (17). For columns close to the center of the magnet, large values of this ratio imply a ghosting pixel at location (n 1 ,n 2 ).
- the second criterion becomes more or less inconclusive, and other ways must be found to overcome the ambiguity problem of the first criterion.
- the present invention uses the apriori knowledge about the approximate shape of the phase difference function in order to resolve this ambiguity. Detailed experimental procedures for obtaining the phase difference function was described in the Background section above. Unlike that "look up" table approach, the present invention does not require detailed and exact values of the phase difference function. In fact, the algorithm of the present invention only needs to know as much about ⁇ (n 1 ,n 2 ) as to make binary decisions.
- the ghosting pixel detection part is rather hueristic.
- the following measures are preferably employed:
- this integer has been chosen to be 8.
- ⁇ is set to zero when the magnitude of its estimated value exceeds a certain threshold.
- the optimal value for this threshold was found empirically from the approximate shape of the phase difference function for various test objects. For the program listed in Appendix (A), this threshold was set to 0.08.
- a second measure taken to improve the robustness of the algorithm is to discard ghosting pixels whose least-square residue is too large. Specifically, if i 1 ,i 2 , . . . , i upper ⁇ N/2and j 1 ,j 2 , . . . , j lower ⁇ N/2 denote the indices of the ghosting pixels of the n 1 th column, taking into account equation (12), the linear least-squares estimation of ⁇ and ⁇ consists of solving the following overdetermined linear system of equations: ##EQU14##
- threshold "mse” are discarded.
- the "-m” option sets the threshold "mse". Appropriate values for the "-m” option can range anywhere between 1 and 3. Clearly, if “mse” is too small, then most of the already detected ghosting pixels will be discarded for the second estimation process. On the other hand, if “mse” is too large, picels which have been misclassified as ghosting ones are not discarded and therefore result in large amounts of error in observations used for the linear least-squares estimation process. In most of the examples of the next section, the "-m” option is set to 2.
- the ghost detection part of the algorithm first checks the ratio between the magnitudes of even and odd parts of the pixel at location (n 1 ,n 2 ). If this ration is close to 1 (or more specifically is in the range [1/eoratio, eoratio]) then either Y(n 1 ,n 2 ) or Y(n 1 ,(n 2 +N/2) mod N) are classified as ghosting pixels. If the phase difference function is less than ⁇ then the magnitude of the ghost (i.e. the ghosted pixel) is smaller than that of the object (i.e. the ghosting pixel).
- phase difference function is larger than ⁇
- the magnitude of the ghost becomes larger than that of the object causing it. Since we expect the phase difference function to be small (less than ⁇ ) in the center of the magnet, the differentiation between ghosting and ghosted pixels is straightforward for the central columns of the image, and therefore there is not any ambiguity in computing the phase difference function. In fact, as we mentioned earlier, the "-t" option takes advantage of this in order to detect/differentiate ghosting and ghosted pixels for the central 30 columns.
- phase difference function For columns away from the center, the phase difference function might become larger than ⁇ , thus creating an ambiguity about the ghosting and ghosted pixels. To resolve this ambiguity, the operator has to provide the algorithm with a clue as to whether or not the phase difference function is larger than ⁇ . Fortunately, this is a simple visual task since in the areas of image with large phase difference function (i.e. larger than ⁇ ) the ghosts are brighter than the actual object causing the ghost. Therefore, if the ghost has larger intensity than the object in the areas to the left of central columns, "-h” option must be set to 1. Similarly, if the ghost has larger intensity than the object in the areas to the right of central columns, "-h” option must be set to 3.
- the ghost has lower intensity than the actual object itself, and thus there is no need to set the "-h” option to any value.
- the ghosts become larger than the objects and the "-h” option is needed to guide the program to correct them.
- the "-d” option sets the internal double precision parameter "smooth” which smoothes the values of for neighboring columns. Specifically, if the value of for the n 1 th column is different from those of the past four columns by more than an amount specified by "smooth", then ⁇ (n 1 ) and ⁇ (n 1 ) are discarded and the n 1 ,th column appears unchanged in the output image Appropriate values for "smooth" can range between 0.3 and 2. Clearly, if "-d” option is set to a small value, e.g. 0.3, then ⁇ and ⁇ for most columns will be discarded and the final output will resemble the ghosted input image to a great extent. On the other hand, if "-d” option is set to a large value like 2, then the amount of smoothing is minimized, and the final image might have some columns which stand out amont their neighboring columns because of their drastically, different values of ⁇ and ⁇ .
- the "-b” option sets the internal double precision parameter "betasmth” which smoothes the values of ⁇ for neighboring columns.
- the functional description of this variable is similar to that of the "-d” option. Appropriate values for "betasmth” however, can range between 0.01 and 1.
- the "-f" flag determines whether or not the processed ghost-free image needs to be rearranged so that the center of the magnet coincides with the center of the image. This flag is set for all the examples shown in the next section.
- the "-a” option sets the internal double variable "scale” which scales the processed image before it is written in the output file. This parameter is normally set anywhere between 500 and 1000.
- the "-e” option sets the internal variable "expand" which expands the final output image by an integer in each direction.
- the expansion is basically done by repeating each pixel a fixed number of times in x and y directions.
- the "-c" flag determines whether the processed image is written in binary or hexadecimal format.
- the hexadecimal format is necessary for generating halftone images with PostScript commands and the Apple LaserWriter.
- Inputfile denotes the name of the input file which contains the ASCII characters representing the time raw data or its two-dimensional inverse Fourier transform. If such an input file does not exist, the program exists while printing "input file does not exist”.
- Outputfile denotes the name of the output file which contains numbers between 0 and 255 representing the processed image.
- the format of these numbers is either in binary or hexadecimal depending on whether or not the "-c" flag is set.
- FIGS. 4-10 Examples of images processed by the ghost elimination algorithm are shown in FIGS. 4-10. For each example, the ghosted image, the processed ghost-free image, and the parameters used with the algorithm will be shown.
- FIG. 4a shows a ghosted heart image which was processed by the ghost elimination algorithm with the following parameters:
- the processed ghost-free version is shown in FIG. 4b.
- the AGC algorithm has done an excellent job of removing the ghosts.
- the magnitude of the ghost in the left side of FIG. 4a is larger than that of the object causing it. Therefore, the parameter "-h" had to be set at 1 in order to remove the ambiguity in the phase difference function for the columns to the left of the image.
- FIG. 5 The second example of the ghost elimination algorithm is shown in FIG. 5.
- the original ghosted heart image is shown in FIG. 5a, and its processed ghost-free version is shown in FIG. 5b.
- the parameters of the algorithm were:
- FIG. 6a A third example of the algorithm is shown in FIG. 6a, and its processed ghost-free version is shown in FIG. 6b.
- the parameters of the algorithm were:
- FIG. 7 A fourth example of the algorithm is shown in FIG. 7.
- the original ghosted heart image is shown in FIG. 7a, and its processed ghost-free version is shown in FIG. 7b.
- the parameters of the algorithm were:
- the magnitude of the ghost in the right and left part of the ghosted image is slightly larger than that of the object causing it. Therefore, the "-h" option is set at 3, to remove the ambiguity associated with the phase difference function.
- FIG. 8a A fifth example of the algorithm is shown in FIG. 8.
- FIG. 8b A fifth example of the algorithm is shown in FIG. 8.
- the original ghosted heart image is shown in FIG. 8a
- its processed ghost-free version is shown in FIG. 8b.
- the parameters of the algorithm were:
- the input file contained the 2-D inverse Fourier transform of the raw time date. Therefore, the "-s" option had to be set at a different value from the previous examples.
- FIG. 9 A sixth example of the algorithm is shown in FIG. 9.
- the original ghosted heart image is shown in FIG. 9a, and its processed ghost-free version is shown in FIG. 9b.
- the parameters of the algorithm were:
- FIG. 10a A seventh example of the algorithm of the algorithm is shown in FIG. 10.
- FIG. 10b A seventh example of the algorithm of the algorithm is shown in FIG. 10.
- the parameters of the algorithm were:
- FIG. 11 An eighth example of the algorithm is shown in FIG. 11.
- the original ghosted heart image is shown in FIG. 11a, and its processed ghost-free version is shown in FIG. 11b.
- the parameters of the algorithm were:
Abstract
Description
x(n.sub.1,n.sub.2 +N/2)=0
correct -g -t100. -r1.5 -s5. -m2. -f -d.7 -b.04 -a750 -e4 inputfile outputfile
|x(n.sub.1,n.sub.2)|>>0
|x(n.sub.1,(n.sub.2 +N/2) mod N)|≈0
|Y.sub.even (n.sub.1,n.sub.2)|=|Y.sub.odd (n.sub.1,n.sub.2)|=|A(n.sub.1,n.sub.2)|=x(n.sub.1,n.sub.2) (14)
correct -g -t100. -r1.5 -s5. -m3. -h1 -f -d2. -b1. -a1000 -e4 htnum htproc
correct -g -t100. -r1.5 -s5. -m2. -f -d1. -b.05 -a1000 -e4 heart5num heart5proc
correct -g -t100. -r1.5 -s5. -m2. -f -d2. -b.1 -h1 -a750 -e4 heart4num heart4proc
correct -g -t100. -r1.5 -s5. -m2. -f -d.7 -b.03 -h3 -a500 -e4 heart3num heart3proc
correct -t10. -r1.3 -s200000000. -m2. -f -d.5 -b1. -a1000 -e4 newhtnum newhtproc
correct -g -t1. -r1.5 -s5. -m3. -f -d.6 -b.06 -a1000 e4 lvrnum lvrproc
correct -g -t100. -r1.5 -s5. -m2. -f -d1. -b.1 -a1000 -e4 body2num body2proc
correct -g -t100. -r1.5 -s5. -m3. -f -d.7 -b.06 -a1000 -e4 body3num body3proc
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US08/198,866 USRE36679E (en) | 1989-08-07 | 1994-02-18 | Method of cancelling ghosts from NMR images |
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US07/390,075 US5089778A (en) | 1989-08-07 | 1989-08-07 | Method of cancelling ghosts from NMR images |
US08/198,866 USRE36679E (en) | 1989-08-07 | 1994-02-18 | Method of cancelling ghosts from NMR images |
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US08/198,866 Expired - Lifetime USRE36679E (en) | 1989-08-07 | 1994-02-18 | Method of cancelling ghosts from NMR images |
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Cited By (11)
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US6321107B1 (en) * | 1999-05-14 | 2001-11-20 | General Electric Company | Determining linear phase shift in conjugate domain for MR imaging |
US6556009B2 (en) | 2000-12-11 | 2003-04-29 | The United States Of America As Represented By The Department Of Health And Human Services | Accelerated magnetic resonance imaging using a parallel spatial filter |
US6701016B1 (en) * | 2000-12-22 | 2004-03-02 | Microsoft Corporation | Method of learning deformation models to facilitate pattern matching |
US6771067B2 (en) | 2001-04-03 | 2004-08-03 | The United States Of America As Represented By The Department Of Health And Human Services | Ghost artifact cancellation using phased array processing |
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US6321107B1 (en) * | 1999-05-14 | 2001-11-20 | General Electric Company | Determining linear phase shift in conjugate domain for MR imaging |
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