Dynamic image reconstruction with tight frame learning
View Patent ↗A computer-implemented method for learning a tight frame includes acquiring undersampled k-space data over a time period using an interleaved process. An average of the undersampled k-space data is determined and a reference image is generated based on the average of the undersampled k-space data. Next, a tight frame operator is determined based on the reference image. Then, a reconstructed image data is generated from the undersampled k-space data via a sparse reconstruction which utilizes the tight frame operator.
1. A computer-implemented method for reconstructing an image based on a learned tight frame, the method comprising:
acquiring undersampled k-space data over a time period using an interleaved process;
determining an average of the undersampled k-space data;
generating a reference image based on the average of the undersampled k-space data;
determining a tight frame operator based on the reference image; and
generating a reconstructed image data from the undersampled k-space data via a sparse reconstruction which utilizes the tight frame operator,
wherein determining a tight frame operator based on the reference image comprises:
determining a reference vector based on the reference image;
initializing one or more tight frame filters using an existing tight frame system; and
performing an iterative process comprising:
defining an analysis operator based on the tight frame filters,
determining a coefficient vector comprising a plurality of tight frame coefficients by applying the analysis operator to the reference vector,
updating the coefficient vector by applying a hard thresholding operator to the tight frame coefficients, and
updating the tight frame filters based on the updated coefficient vector.
2. The method of claim 1 , wherein the interleaved process samples lines of k-space data at a predetermined sampling rate.
3. The method of claim 1 , wherein the average of the undersampled k-space data is determined in a temporal direction based on the time period.
4. The method of claim 1 , wherein generating the reference image based on the average of the undersampled k-space data comprises:
applying a Fourier transformation to the average of the undersampled k-space data.
5. The method of claim 1 , wherein determining the reference vector based on the reference image comprises:
concatenating columns of the reference image vertically together to yield the reference vector.
6. The method of claim 1 , wherein the tight frame filters are updated using a Singular Vector Decomposition process.
7. The method of claim 1 , wherein the iterative process is repeated a number of times equal to a predetermined user-selected iteration number.
8. The method of claim 1 , wherein the tight frame operator is used as a regularization term in the sparse reconstruction.
9. The method of claim 1 , wherein the tight frame operator is further determined based on one or more additional reference images.
10. An article of manufacture for reconstructing an image based on a learned tight frame, the article of manufacture comprising a non-transitory, tangible computer-readable medium holding computer-executable instructions for performing a method comprising:
acquiring undersampled k-space data over a time period using an interleaved process;
determining an average of the undersampled k-space data;
generating a reference image based on the average of the undersampled k-space data;
determining a tight frame operator based on the reference image; and
generating a reconstructed image data from the undersampled k-space data via a sparse reconstruction which utilizes the tight frame operator,
wherein determining a tight frame operator based on the reference image comprises:
determining a reference vector based on the reference image;
initializing one or more tight frame filters using an existing tight frame system; and
performing an iterative process comprising:
defining an analysis operator based on the tight frame filters,
determining a coefficient vector comprising a plurality of tight frame coefficients by applying the analysis operator to the reference vector,
updating the coefficient vector by applying a hard thresholding operator to the tight frame coefficients, and
updating the tight frame filters based on the updated coefficient vector.
11. The article of manufacture of claim 10 , wherein the average of the undersampled k-space data is determined in a temporal direction based on the time period.
12. The article of manufacture of claim 10 , wherein determining the reference vector based on the reference image comprises:
concatenating columns of the reference image vertically together to yield the reference vector.
13. The article of manufacture of claim 10 , wherein the tight frame filters are updated using a Singular Vector Decomposition process.
14. The article of manufacture of claim 10 , wherein the iterative process is repeated a number of times equal to a predetermined user-selected iteration number.
15. The article of manufacture of claim 10 , wherein the tight frame operator is used as a regularization term in the sparse reconstruction.
16. The article of manufacture of claim 10 , wherein the tight frame operator is further determined based on one or more additional reference images.