Highly undersampled magnetic resonance image reconstruction via homotopic l0-minimization

IEEE Transactions on Medical Imaging

Volumn 28, Issue 1, 2009, Pages 106-121

  Trzasko, Joshua ^a   Manduca, Armando ^a  

^a Mayo Clinic   (United States)

Author keywords

Compressed sensing; Compressive sensing (CS); Image reconstruction; Magnetic resonance imaging (MRI); Nonconvex optimization

Indexed keywords

ATOMS; IMAGE PROCESSING; IMAGE RECONSTRUCTION; MAGNETIC MATERIALS; MAGNETIC RESONANCE; MAGNETIC RESONANCE IMAGING; OPTIMIZATION; PHOTOACOUSTIC EFFECT; REPAIR; RESTORATION; SIGNAL RECONSTRUCTION;

COMPRESSED SENSING; COMPRESSIVE SENSING; COMPRESSIVE SENSING (CS); CS METHODS; EXACT RECONSTRUCTIONS; K SPACES; MINIMIZATION PROBLEMS; MR IMAGES; MRI RECONSTRUCTIONS; NONCONVEX OPTIMIZATION; NYQUIST LIMITS; PATIENT COMFORTS; PHYSIOLOGICAL PROCESSES; POTENTIAL BENEFITS; RECENT DEVELOPMENTS; SAMPLING RATES; SPARSE REPRESENTATIONS; THEORETICAL MINIMUMS; TRANSFORM DOMAINS;

RESONANCE;

ANIMAL; ARTICLE; ARTIFACT; ARTIFICIAL INTELLIGENCE; AUTOMATED PATTERN RECOGNITION; FOURIER ANALYSIS; HISTOLOGY; HUMAN; IMAGE PROCESSING; IMAGE SUBTRACTION; INFORMATION PROCESSING; METHODOLOGY; NUCLEAR MAGNETIC RESONANCE IMAGING; SAMPLE SIZE; SPINE; THREE DIMENSIONAL IMAGING; WRIST;

ANIMALS; ARTIFACTS; ARTIFICIAL INTELLIGENCE; DATA COMPRESSION; FOURIER ANALYSIS; HUMANS; IMAGE PROCESSING, COMPUTER-ASSISTED; IMAGING, THREE-DIMENSIONAL; MAGNETIC RESONANCE IMAGING; PATTERN RECOGNITION, AUTOMATED; SAMPLE SIZE; SPINE; SUBTRACTION TECHNIQUE; WRIST;

EID: 58049195322     PISSN: 02780062     EISSN: None     Source Type: Journal    
DOI: 10.1109/TMI.2008.927346     Document Type: Article

References (45)

1. E. Candes, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information", IEEE Trans. Inf. Theory, vol. 52, no. 2, pp. 489-509, Feb. 2006.
2. D. Donoho, "Compressed sensing", IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289-1306, Apr. 2006.
3. P. Mansfield, "Multiplanar image formation using NMR spin echos", J. Phys. C, vol. 10, pp. 349-352, 1977.
4. E. Haacke, E. Lindskog. and W. Lin, "A fast, iterative, partial-Fourier technique capable of local phase recovery", J. Magn. Reson., vol. 92, pp. 125-146, 1991.
5. D. Noll, D. Nishimura, and A. Macovski, "Homodyne detection in magnetic resonance imaging", IEEE Trans. Med. Imag., vol. 10, no. 2, pp. 154-163, Jun. 1991.
6. E. Candes, L. Demanet, D. Donoho, and L. Ying, "Fast discrete curvelet transforms", Multiscale Modeling Simulation, vol. 5, no. 3, pp. 861-899, 2006.
7. H. Rauhut, K. Schnass, and P. Vandergheynst, "Compressed sensing and redundant dictionaries", IEEE Trans. Inf. Theory, vol. 54, no. 5, pp. 2210-2219, May 2006.
8. E. Candes and T. Tao. "Decoding by linear programming", IEEE Trans. Inf. Theory, vol. 51, no. 12, pp. 4203-4215, Dec. 2005.
9. E. Candes and T. Tao, "Near-optimal signal recovery from random projections: Universal encoding strategies?", IEEE Trans. Inf. Theory, vol. 52, no. 12, pp. 5406-5425, Dec. 2006.
10. M. Rudelson and R. Vershynin, "Sparse reconstruction by convex relaxation: Fourier and Gaussian measurements." in Proc. 40th Annu. Conf. Inf. Sci. Syst., Princeton, NJ, 2006, pp. 207-212.
11. R. DeVore, "Deterministic constructions of compressed sensing matrices", J. Complexity, vol. 23, no. 4-6, pp. 918-925, Aug.-Dec. 2007.
12. W. Bajwa, J. Haupt, A. Sayeed, and R. Nowak, "Toeplitz-structured compressed sensing matrices", in Proc. IEEE Workshop Stat. Signal Process., Aug. 2007, pp. 294-298.
13. M. Lusdg, D. Donoho, and J. Pauly, "Sparse MRI: The application of compressed sensing for rapid MR imaging", Magn. Reson. Med., vol. 59, no. 6, pp. 1182-1195. Dec. 2007.
14. J. Ye, S. Tak, Y. Han, and H. Park, "Projection reconstruction MR imaging using FOCUSS", Magn. Reson. Med., vol. 57, pp. 764-775, 2007.
15. E. Candes and J. Romberg, "Practical signal recovery from random projections", in Proc. SPIE Int. Symp. Electron. Imag.: Computational Imag. III, San Jose, CA, Jan. 2005, pp. 76-86.
16. E. Candes, J. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements", Commun. Pure Appl. Math., vol. 59, pp. 1207-1223, 2006.
17. K. Block, M. Uecker, and J. Frahm, "Undersampled radial MRI with multiple coils, iterative image reconstruction using a total variation constraint"., Magn. Reson. Med., vol. 57, pp. 1086-1098, 2007.
18. M. Lustig, J. Santos, D. Donoho, and J. Pauly, "k-t SPARSE: High frame rate dynamic MRI exploiting spatio-temporal sparsity", in Proc. ISMRM, Seattle, WA, May 2006, p. 2420.
19. S. Kim, K. Koh, M. Lustig, and S. Boyd, "An interior-point method for large-scale 11-regularized least squares", IEEE J. Selected Topics Signal Process., vol. 1, no. 4, pp. 606-617, Dec. 2007.
20. L. He, T. Chang, S. Osher, T. Fang, and P. Speier, MR image reconstruction by using the iterative refinement method and nonlinear inverse scale space methods UCLA CAM Rep., 2006.
21. H. Jung, J. Ye, and E. Kim, "Improved k-t blast and k-t SENSE using FOCUSS", Phys. Med. Biol., vol. 52, pp. 3201-3226, 2007.
22. R. Chartrand, "Exact reconstruction of sparse signal via nonconvex minimization", IEEE Signal Process. Lettt., vol. 14, no. 10, pp. 707-710, Oct. 2007.
23. P. Huber, Robust Statistics. New York: Wiley. 1981.
24. D. Geman and G. Reynolds, "Nonlinear image recovery with halfquadratic regularization", IEEE Trans. Image Process., vol. 4, no. 7, pp. 932-946, Jul. 1995.
25. M. Nikolova and R. Chan, "The equivalence of half-quadratic minimization and the gradient linearization iteration", IEEE Trans. Image Process., vol. 16, no. 6, pp. 1623-1627, Jun. 2007.
26. E. Candes, N. Braun, and M. Wakin, "Sparse signal and image recovery from compressive samples", in Proc. IEEE Int. Symp. Biomed. Imag., Arlington, VA, Apr. 2007, pp. 976-979.
27. P. Perona and J. Malik, "Scale-space and edge detection using anisotropic diffusion", IEEE Trans. Pattern Anal. Mach Intell., vol. 12, no. 7, pp. 629-639, Jul. 1990.
28. M. Black, G. Sapiro, D. Marimon, and D. Heeger, "Robust anisotropic diffusion", IEEE Trans. Image Process., vol. 7, no. 3, pp. 421-432, Mar. 1998.
29. Y. Leclerc, "Constructing simple stable descriptions for image partitioning", Int. J. Comput. Vis., vol. 3, no. 1, pp. 73-102, 1989.
30. N. Saito, "Superresolution of noisy band-limited data by data adaptive regularization and its application to seismic trace inversion", in Proc. ICASSP, Albuquerque, NM, Apr. 1990, pp. 1237-1240.
31. A. Delaney and Y. Bresler, "Globally convergent edge-preserving reguarlized reconstruction: An application to limited-angle tomography", IEEE Trans. Image Process., vol. 7. no. 2, pp. 204-231, Feb. 1998.
32. D. Yu and J. Fessler, "Edge-preserving tomographic reconstruction with nonlocal regularization", IEEE Trans. Med. Imag., vol. 21. no. 2, pp. 159-173, Feb. 2002.
33. J. Trzasko, A. Manduca, and E. Borisch, "Sparse MRI reconstruction via multiscale 10 continuation", in Proc. IEEE Workshop Stat. Signal Process., Aug. 2007, pp. 176-180.
34. J. Nocedal and S. Wright, Numerical Optimization. New York: Springer, 2006.
35. A. Blake and A. Zisserman, Visual Reconstruction.: MIT Press, 1987.
36. J. Wood and K. Johnson, "Wavelet-packet denoising of magnetic resonance images: Importance of Rician statistics at low SNR", Magn. Reson. Med., vol. 41, pp. 631-635, 1999.
37. J. Fessler and D. Noll, "Iterative image reconstruction in MRI with separate magnitude and phase regularization", in IEEE Int. Symp. Biomed. Imag., Apr. 2004, pp. 209-212.
38. K. Pruessmann, M. Weiger, M. Scheidegger, and P. Boesiger, "SENSE: Sensitivity encoding for fast MRI", Magn. Reson. Med., vol. 42, pp. 952-962, 1999.
39. A. Papoulis, "Generalized sampling expansion", IEEE Trans. Circuits Syst., vol. 24, no. 11, pp. 652-654, Nov. 1977.
40. H. Hu, A. Madhuranthakam, D. Kruger, J. Glockner, and S. Riederer, "Combination of 2-D sensitivity encoding and 2-D partial Fourier techniques for improved acceleration in 3-D contrast-enhanced MR angiorgaphy", Magn. Reson. Med., vol. 55, pp. 16-22, 2005.
41. A. Raj, G. Singh, R. Zabih, B. Kressler, Y. Wang, N. Schuff. and M. Weiner, "Bayesian parallel imaging with edge-preserving priors", Magn. Reson. Med., vol. 57, pp. 8-21, 2007.
42. D. Luenberger, Linear and Nonlinear Programming, 2nd ed. Boston, MA: Kluwer, 2003.
43. P. Boufounos, M. Duarte, and R. Baraniuk, "Sparse signal reconstruction from noisy compressive measurements using cross validation", in Proc. IEEE Workshop Stat. Signal Process., Aug. 2007, pp. 299-303.
44. C. Vogel, Computational methods for inverse problems. Philadelphia, PA: SIAM, 2002.
45. E. Candes, "The uniform uncertainty principle", presented at the IMA short course: Compressive sampling and frontiers in signal processing, Minneapolis, MN, Jun. 2007.