Method and system for parallel reconstruction in the K-space domain for application in imaging systems
View Patent ↗A method of performing parallel image reconstruction of undersampled image data in k-space. A defined partitioning of a k-space region into a plurality of segments is received. A segment of the plurality of segments is identified wherein data is sampled at less than a Nyquist rate. First imaging data is sampled at the Nyquist rate. A reconstruction coefficient is calculated for at least a portion of the identified segment using the sampled first imaging data. Second imaging data is sampled at less than the Nyquist rate. A value for a missing k-space sample in the identified segment is predicted using the calculated reconstruction coefficient and the sampled second imaging data. An image of the image area is defined using the predicted value and the received second dataset.
1. A system for performing parallel image reconstruction of undersampled image data in k-space, the system comprising:
an imaging apparatus configured to generate first imaging data of an image area and to generate second imaging data of the image area;
a computer-readable medium having computer-readable instructions therein, the instructions comprising
receiving a defined partitioning of a k-space region into a plurality of segments;
identifying a segment of the plurality of segments wherein data is sampled at less than a Nyquist rate;
sampling the generated first imaging data at the Nyquist rate;
calculating a reconstruction coefficient for at least a portion of the identified segment using the sampled first imaging data;
sampling the identified segment of the generated second imaging data at less than the Nyquist rate;
predicting a value for a missing k-space sample in the identified segment using the calculated reconstruction coefficient and the sampled second imaging data; and
defining an image of the image area using the predicted value and the sampled second imaging data; and
a processor operably coupled to the computer-readable medium and configured to execute the instructions.
2. A non-transitory computer-readable medium having computer-readable instructions therein that, upon execution by a processor, cause the processor to perform parallel image reconstruction of undersampled image data in k-space, the instructions comprising:
receiving a defined partitioning of a k-space region into a plurality of segments;
identifying a segment of the plurality of segments wherein data is sampled at less than a Nyquist rate;
sampling the first imaging data at the Nyquist rate;
calculating a reconstruction coefficient for at least a portion of the identified segment using the sampled first imaging data;
sampling the identified segment of the second imaging data at less than the Nyquist rate;
predicting a value for a missing k-space sample in the identified segment using the calculated reconstruction coefficient and the sampled second imaging data; and
defining an image of the image area using the predicted value and the received second dataset.
3. A method of performing parallel image reconstruction of undersampled image data in k-space, the method comprising:
(a) receiving, at a computing device, a defined partitioning of a k-space region into a plurality of segments;
(b) identifying, by the computing device, a segment of the plurality of segments wherein data is sampled at less than a Nyquist rate;
(c) sampling, by the computing device, the first imaging data at the Nyquist rate;
(d) calculating, by the computing device, a reconstruction coefficient for at least a portion of the identified segment using the sampled first imaging data;
(e) sampling, by the computing device, the identified segment of the second imaging data at less than the Nyquist rate;
(f) predicting, by the computing device, a value for a missing k-space sample in the identified segment using the calculated reconstruction coefficient and the sampled second imaging data; and
(g) defining, by the computing device, an image of the image area using the predicted k-space value and the received second dataset.
4. The non-transitory computer-readable medium of claim 2 , further comprising repeating (a)-(g) for a plurality of timeframes.
5. The non-transitory computer-readable medium of claim 2 , wherein calculating the reconstruction coefficient uses a portion of the sampled first imaging data corresponding to the identified segment.
6. The non-transitory computer-readable medium of claim 2 , wherein the segment comprises a plurality of identified segments.
7. The non-transitory computer-readable medium of claim 6 , wherein sampling of the plurality of identified segments at less than the Nyquist rate is uniform across the plurality of identified segments.
8. The non-transitory computer-readable medium of claim 6 , wherein sampling of the plurality of identified segments at less than the Nyquist rate is variable across the plurality of identified segments.
9. The non-transitory computer-readable medium of claim 2 , wherein the plurality of segments are defined in a phase-encoding direction or in a frequency encoding direction.
10. The non-transitory computer-readable medium of claim 2 , wherein the plurality of segments are defined in a phase-encoding direction and in a frequency encoding direction.
11. The non-transitory computer-readable medium of claim 10 , wherein the plurality of segments are defined into a first segment on a first side of a central phase-encoding segment and a second segment on a second side of the central phase-encoding segment, wherein the second side is opposite the first side.
12. The non-transitory computer-readable medium of claim 11 , wherein the plurality of segments are defined into a third segment on a third side of a central frequency-encoding segment and a fourth segment on a fourth side of the central frequency-encoding segment, wherein the fourth side is opposite the third side.
13. The non-transitory computer-readable medium of claim 11 , wherein sampling of the central phase-encoding segment is at a rate that is greater than or equal to the Nyquist rate.
14. The non-transitory computer-readable medium of claim 13 , wherein the central phase-encoding segment of the second imaging data is not used to predict the value.
15. The non-transitory computer-readable medium of claim 10 , wherein the plurality of segments are defined into a first plurality of segments on a first side of a central phase-encoding segment and a second plurality of segments on a second side of the central phase-encoding segment, wherein the second side is opposite the first side.
16. The non-transitory computer-readable medium of claim 15 , wherein a width of the first plurality of segments increases from a low to a high spatial frequency in the phase-encoding direction.
17. The non-transitory computer-readable medium of claim 15 , wherein the plurality of segments are defined into a third plurality of segments on a third side of a central frequency-encoding segment and a fourth plurality of segments on a fourth side of the central frequency-encoding segment, wherein the fourth side is opposite the third side.
18. The non-transitory computer-readable medium of claim 17 , wherein a width of the third plurality of segments increases from a low to a high spatial frequency in the frequency-encoding direction.
19. The non-transitory computer-readable medium of claim 6 , wherein predicting the value for the identified segment comprises
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where n is a segment number of the identified segment, i is a coil number, m is a first offset of the missing k-space sample from an acquired sample in the identified segment of the second imaging data, k x is a first index of the missing k-space sample in a frequency-encoding direction, k y is a second index of the missing k-space sample in a phase-encoding direction, Δk x is a first spacing between k-space measurements at the Nyquist rate in the frequency-encoding direction, Δk y is a second spacing between k-space measurements at the Nyquist rate in the phase-encoding direction, a first index a q and a second index b q count through a number of blocks N b included in a reconstruction, N c is a number of receiver coils, w(n, i, j, m, q) is a reconstruction coefficient obtained for coil number i, for segment number n, and for first offset m, and S j (k x +a q Δk x ,k y +b q Δk y )is a k-space signal in segment number n of coil number i at a point (k x +a q Δk x ,k y +b q Δk y ).
20. The non-transitory computer-readable medium of claim 19 , wherein calculating the reconstruction coefficient comprises solving
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for the reconstruction coefficient, w(n, i, j, m, q) using a Moore-Penrose pseudo-inverse.