An algorithm for sparse MRI reconstruction by Schatten p-norm minimization

Magnetic Resonance Imaging

Volumn 29, Issue 3, 2011, Pages 408-417

  Majumdar, Angshul ^a   Ward, Rabab K ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Compressed sensing based methods; K space; Schatten p norm minimization

Indexed keywords

ALGORITHM; ARTICLE; CONTROLLED STUDY; CORRELATION COEFFICIENT; DIAGNOSTIC ACCURACY; FOURIER TRANSFORMATION; IMAGE ANALYSIS; IMAGE PROCESSING; IMAGE RECONSTRUCTION; NEUROIMAGING; NUCLEAR MAGNETIC RESONANCE IMAGING; PRIORITY JOURNAL; PROBLEM SOLVING; PROCESS OPTIMIZATION;

ALGORITHMS; DATA INTERPRETATION, STATISTICAL; HUMANS; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; MAGNETIC RESONANCE IMAGING; REPRODUCIBILITY OF RESULTS; SAMPLE SIZE; SENSITIVITY AND SPECIFICITY;

EID: 79952534049     PISSN: 0730725X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mri.2010.09.001     Document Type: Article

References (45)

1. Lustig M., Donoho D.L., Pauly J.M. Sparse MRI: the application of compressed sensing for rapid MR imaging. Magn Reson Med 2007, 58(6):1182-1195.
2. Qu X., Zhang W., Guo D., Cai C., Cai S., Chen Z. Iterative thresholding compressed sensing MRI based on contourlet transform 2010.
3. Haldar J.P., Hernando D., Liang Z.P. Compressed-sensing MRI with random encoding Available at:. http://coil.ifp.uiuc.edu/documents/preprint_non_Fourier_CS-MRI.pdf.
4. Chen L., Schabel M.C., DiBella E.V.R. Reconstruction of dynamic contrast enhanced magnetic resonance imaging of the breast with temporal constraints. Magn Reson Med 2010, 28(5):637-645.
5. Peng H., Sabati M., Lauzon L., Frayne R. MR image reconstruction of sparsely sampled 3D k-space data by projection-onto-convex sets. Magn Reson Med 2006, 24(6):761-773.
6. Jung H., Sung K., Nayak K.S., Kim E.Y., Ye J.C. k-t FOCUSS: a general compressed sensing framework for high resolution dynamic MRI. Magn Reson Med 2009, 61(1):103-116.
7. Gamper U., Boesiger P., Kozerke S. Compressed sensing in dynamic MRI. Magn Reson Med 2008, 59(2):365-373.
8. http://en.wikipedia.org/wiki/Schatten_norm.
9. Erickson B.J., Manduca A., Palisson P., Persons K.R., Earnest F., Savcenko V., et al. Wavelet compression of medical images. Radiology 1998, 206(3):599-607.
10. Tolba A.S. Wavelet packet compression of medical images. Digital Signal Processing 2002, 12(4):441-470.
11. Wang H., Rosenfeld D., Braun M., Yan H. Compression and reconstruction of MRI images using 2D DCT. Magn Reson Med 1992, 10(3):427-432.
12. Sanchez V., Nasiopoulos P., Abugharbieh R. Efficient lossless compression of 4-D medical images based on the advanced video coding scheme. IEEE Trans Inf Technol Biomed 2008, 12(4):442-446.
13. Singh S., Kumar V., Verma H.K. DWT-DCT hybrid scheme for medical image compression. J Med Eng Technol 2007, 31(2):109-122.
14. Chen Y.Y. Medical image compression using DCT-based subband decomposition and modified SPIHT data organization. Int J Med Inform 2007, 76(10):717-725.
15. Amaldi E., Kann V. On the approximability of minimizing nonzero variables or unsatisfied relations in linear systems,. Theoretical Computer Science 1998, 209:237-260.
16. Candès E.J., Romberg J., Tao T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inf Theory 2006, 52(2):489-509.
17. Chartrand R., Staneva V. Restricted isometry properties and nonconvex compressive sensing. Inverse Probl 2008, 24(035020):1-14.
18. Trzasko J., Manduca A. Highly undersampled magnetic resonance image reconstruction via homotopic l0-minimization. IEEE Trans Med Imaging 2009, 28(1):106-121.
19. Majumdar A., Ward R.K. Under-determined non-Cartesian MR reconstruction with non-convex sparsity promoting analysis prior. Med Image Comput Comput Assist Interv. 2010, 13(Pt 3):513-520.
20. Chartrand R. Fast algorithms for nonconvex compressive sensing: MRI reconstruction from very few data. IEEE Int Symp Biomed Imaging 2009, 262-265.
21. Baeza I., Verdoy J.A., Villanueva R.J., Oller J.V. SVD lossy adaptive encoding of 3D digital images for ROI progressive transmission. Image Vis Comput 2010, 28(3):449-457.
22. Al-Fayadh A., Hussain A.J., Lisboa P., Al-Jumeily D. An adaptive hybrid image compression method and its application to medical images. ISBI 2008, 237-240.
23. Dologlou I., van Ormondt D., Carayannisb G. MRI scan time reduction through non-uniform sampling and SVD-based estimation. Signal Process 1996, 55(2):207-219.
24. Recht B., Xu W., Hassibi B. Necessary and sufficient conditions for success of the nuclear norm heuristic for rank minimization. 47th IEEE Conference on Decision and Control 2008, 3065-3070.
25. Recht B., Xu W., Hassibi B. Null space conditions and thresholds for rank minimization. Math Program 2010, Available at: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.150.6296.
26. Recht B, Fazel M, Parrilo PA Guaranteed minimum rank solutions to linear matrix equations via nuclear norm minimization. SIAM Rev 2010, 52(3):471-501.
27. Dvijotham K., Fazel M. A nullspace analysis of the nuclear norm heuristic for rank minimization 2010.
28. Candès E.J., Tao T. The power of convex relaxation: near-optimal matrix completion. IEEE Trans Inf Theory 2009, 56(5):2053-2080.
29. Saab R., Yilmaz O. Sparse recovery by non-convex optimization - instance optimality. Appl Comput Harmon Anal 2010, 29(1):30-48.
30. Mohan K., Fazel M. Reweighted nuclear norm minimization with application to system identification 2010, 2953-2959.
31. Candes E.J., Wakin M.B., Boyd S. Enhancing sparsity by reweighted l1 minimization. J Fourier Anal Appl 2008, 14:877-905.
32. Zaroubi S., Goelman G. Complex denoising of MR data via wavelet analysis: application for functional MRI. Magn Reson Med 2000, 18(1):59-68.
33. Anand C.S., Sahambi J.S. Wavelet domain non-linear filtering for MRI denoising. Magn Reson Med 2010, 28(6):842-861.
34. Do T.T., Chen Y., Nguyen N., Ganz L., Tran T.D. A fast and efficient heuristic nuclear-norm algorithm for affine rank minimization. ICASSP 2009, 3393-3396.
35. R Meka, P Jain, IS Dhillon. Guaranteed rank minimization via singular value projection, arXiv:0909.5457v3.
36. Ji S., Ye J. An accelerated gradient method for trace norm minimization. Proceedings of the 26th Annual International Conference on Machine Learning 2009, 457-464.
37. http://cnx.org/content/m32168/latest/.
38. Selesnick I.W., Figueiredo M.A.T. Signal restoration with overcomplete wavelet transforms: comparison of analysis and synthesis priors. Proceedings of SPIE 2009, 7446(Wavelets XIII). Available at: http://spiedl.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PSISDG00744600000174460D000001&idtype=cvips&prog=normal.
39. Lin T., Herrmann F.J. Compressed extrapolation. Geophysics 2007, 72(5):77-93.
40. Zhang S., Block K.T., Frahm J. Magnetic resonance imaging in real time: advances using radial FLASH. J Magn Reson Med 2010, 31(1):101-109.
41. Fessler J.A., Sutton B.P. Nonuniform fast Fourier transforms using min-max interpolation. IEEE Trans Signal Proc 2003, 51(2):560-574.
42. Chartrand R. Exact reconstruction of sparse signals via nonconvex minimization,. IEEE Signal Process Lett 2007, 14:707-710.
43. van den Berg E., Friedlander M.P. Probing the Pareto frontier for basis pursuit solutions. SIAM J Sci Comput 2008, 31(2):890-912.
44. Chartrand R., Yin W. Iteratively reweighted algorithms for compressive sensing. Int Conf Acoust Speech Signal Process 2008, 3869-3872.
45. http://soi.stanford.edu/~rmunk/PROPACK/.