Denoising diffusion-weighted magnitude MR images using rank and edge constraints

Magnetic Resonance in Medicine

Volumn 71, Issue 3, 2014, Pages 1272-1284

  Lam, Fan ^a,b   Babacan, S Derin ^b   Haldar, Justin P ^c   Weiner, Michael W ^d,e   Schuff, Norbert ^d,e   Liang, Zhi Pei ^a,b  

^a University of Illinois at Urbana Champaign   (United States)

^b UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^c University of Southern California   (United States)

^d UNIVERSITY OF CALIFORNIA   (United States)

^e VETERANS AFFAIRS MEDICAL CENTER   (United States)

Author keywords

diffusion tensor imaging; diffusion weighted imaging; edge constraints; low rank approximation; noncentral distribution; Rician distribution

Indexed keywords

APPROXIMATION THEORY; CLUSTERING ALGORITHMS; IMAGE ENHANCEMENT; LEARNING TO RANK; MAGNETIC RESONANCE; MAGNETIC RESONANCE IMAGING; MAXIMUM LIKELIHOOD ESTIMATION; SIGNAL TO NOISE RATIO; SURFACE DIFFUSION; TENSORS;

ALTERNATING MINIMIZATION; DIFFUSION WEIGHTED IMAGES; DIFFUSION WEIGHTED IMAGING; DIFFUSION-WEIGHTED MAGNETIC RESONANCE; EDGE CONSTRAINTS; LOW RANK APPROXIMATIONS; OPTIMIZATION PROBLEMS; RICIAN DISTRIBUTION;

DIFFUSION TENSOR IMAGING;

ALGORITHM; ARTICLE; ARTIFACT REDUCTION; DENOISING DIFFUSION WEIGHTED MAGNITUDE IMAGING; DIFFUSION WEIGHTED IMAGING; HUMAN; IMAGE QUALITY; IN VIVO STUDY; MATHEMATICAL MODEL; NORMAL HUMAN; NUCLEAR MAGNETIC RESONANCE SCANNER; QUALITATIVE ANALYSIS; QUANTITATIVE ANALYSIS; SIGNAL NOISE RATIO; SIMULATION; ANATOMY AND HISTOLOGY; ARTIFACT; BRAIN; COMPUTER ASSISTED DIAGNOSIS; IMAGE ENHANCEMENT; PROCEDURES; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY; STATISTICAL ANALYSIS;

ALGORITHMS; ARTIFACTS; BRAIN; DATA INTERPRETATION, STATISTICAL; DIFFUSION MAGNETIC RESONANCE IMAGING; HUMANS; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY; SIGNAL-TO-NOISE RATIO;

EID: 84894484107     PISSN: 07403194     EISSN: 15222594     Source Type: Journal    
DOI: 10.1002/mrm.24728     Document Type: Article

References (61)

1. Pierpaoli C, Basser PJ,. Toward a quantitative assessment of diffusion anisotropy. Magn Reson Med 1996; 36: 893-906.
2. Jones DK, Basser PJ,. "Squashing peanuts and smashing pumpkins": how noise distorts diffusion-weighted MR data. Magn Reson Med 2004; 52: 979-993.
3. Wang Z, Vemuri BC, Chen Y, Mareci TH,. A constrained variational principle for direct estimation and smoothing of the diffusion tensor field from complex DWI. IEEE Trans Med Imag 2004; 23: 930-939.
4. Haldar JP, Wedeen VJ, Nezamzadeh M, Dai G, Weiner MW, Schuff N, Liang ZP,. Improved diffusion imaging through SNR-enhancing joint reconstruction. Magn Reson Med 2013; 69: 277-289.
5. Gudbjartsson H, Patz S,. The Rician distribution of noisy MRI data. Magn Reson Med 1995; 34: 910-914.
6. Rice SO,. Mathematical analysis of random noise. Bell Syst Tech J 1944; 23: 282-332.
7. Koay CG, Basser PJ,. Analytically exact correction scheme for signal extraction from noisy magnitude MR signals. J Magn Reson 2006; 179: 317-322.
8. Henkelman RM,. Measurement of signal intensities in the presence of noise in MR images. Med Phys 1985; 12: 232-233.
9. Bernstein MA, Thomasson DM, Perman WH,. Improved detectability in low signal-to-noise ratio magnetic resonance images by means of a phase-corrected real reconstruction. Med Phys 1989; 16: 813-817.
10. Constantinides CD, Atalar E, McVeigh ER,. Signal-to-noise measurements in magnitude images from NMR phased arrays. Magn Reson Med 1997; 38: 852-857.
11. Dietrich O, Raya JG, Reeder SB, Ingrisch M, Reiser MF, Schoenberg SO,. Influence of multichannel combination, parallel imaging and other reconstruction techniques on MRI noise characteristics. Magn Reson Imag 2008; 26: 754-762.
12. Aja-Fernandez S, Tristan-Vega A,. Influence of noise correlation in multiple-coil statistical models with sum of squares reconstruction. Magn Reson Med 2012; 67: 580-585.
13. Andersson JLR,. Maximum a posteriori estimation of diffusion tensor parameters using a Rician noise model: why, how and but. NeuroImage 2008; 42: 1340-1356.
14. Descoteaux M, Angelino E, Fitzgibbons S, Deriche R,. Apparent diffusion coefficients from high angular resolution diffusion imaging: estimation and applications. Magn Reson Med 2006; 56: 395-410.
15. Nowak RD,. Wavelet-based Rician noise removal for magnetic resonance imaging. IEEE Trans Image Process 1999; 8: 1408-1419.
16. Aja-Fernandez S, Niethammer M, Kubicki M, Shenton ME, Westin CF,. Restoration of DWI data using a Rician LMMSE estimator. IEEE Trans Med Imag 2008; 27: 1389-1403.
17. Koay CG, Ozarslan E, Basser PJ,. A signal transformational framework for breaking the noise floor and its applications in MRI. J Magn Reson 2009; 197: 108-119.
18. Foi A,. Noise estimation and removal in MR imaging: the variance-stabilization approach. In Proceedings of IEEE International Symposium on Biomedical Imaging, Chicago, Illinois, USA, 2011. pp. 1809-1814.
19. Luisier F, Wolfe PJ,. Chi-square unbiased risk estimate for denoising magnitude MR images. In Proceedings of IEEE ICIP, Brussels, Belgium, 2011. pp. 1561-1564.
20. Basu S, Fletcher T, Whitaker R,. Rician noise removal in diffusion tensor MRI. Med Image Comput Comput Assist Interv 2006; 9: 117-125.
21. McGraw T, Vemuri B, Ozarslan E, Chen Y, Mareci T,. Variational denoising of diffusion weighted MRI. Inverse Prob Imaging 2009; 3: 625-648.
22. Ding Z, Gore JC, Anderson AW,. Reduction of noise in diffusion tensor images using anisotropic smoothing. Magn Reson Med 2005; 53: 485-490.
23. Van Hecke W, Leemans A, De Backer S, Jeurissen B, Parizel PM, Sijbers J,. Comparing isotropic and anisotropic smoothing for voxel-based DTI analyses: a simulation study. Human Brain Mapping 2010; 31: 98-114.
24. Walker-Samuel S, Orton M, Boult JKR, Robinson SP,. Improving apparent diffusion coefficient estimates and elucidating tumor heterogeneity using Bayesian adaptive smoothing. Magn Reson Med 2011; 65: 438-447.
25. Patel V, Shi Y, Thompson PM, Toga AW,. K-SVD for HARDI denoising. In Proceedings of IEEE International Symposium on Biomedical Imaging, Chicago, Illinois, USA, 2011. pp. 1805-1808.
26. Wiest-Daessle N, Prima S, Coupe P, Morrissey SP, Barillot C,. Rician noise removal by non-local means filtering for low signal-to-noise ratio MRI: Applications to DT-MRI. In Proceedings of MICCAI, New York, New York, USA, 2008. pp. 171-179.
27. Descoteaux M, Wiest-Daessle N, Prima S, Barillot C, Deriche R,. Impact of Rician adapted non-local means filtering on HARDI. In Proceedings of MICCAI, 2008. pp. 122-130.
28. Manjon JV, Coupe P, Marti-Bonmati L, Collins DL, Robles M,. Adaptive non-local means denoising of MR images with spatially varying noise levels. J Magn Reson Imag 2010; 31: 192-203.
29. Manjon JV, Thacker NA, Lull JJ, Garcia-Marti G, Marti-Bonmati L, Robles M,. Multicomponent MR image denoising. Int J Biomed Imaging 2009; 2009:Article ID 756897, 10 pages.
30. Liang ZP,. Spatiotemporal imaging with partially separable functions. In Proceedings of IEEE International Symposium on Biomedical Imaging, Washington DC, USA, 2007. pp. 988-991.
31. Haldar JP, Liang ZP,. Spatiotemporal imaging with partially separable functions: a matrix recovery approach. In Proceedings of IEEE International Symposium on Biomedical Imaging, Rotterdam, The Netherlands, 2010. pp. 716-719.
32. Zhao B, Haldar JP,. Christodoulou AG, Liang ZP, Image reconstruction from highly undersampled (k, t)-space data with joint partial separability and sparsity constraints. IEEE Trans Med Imag 2012; 31: 1809-1820.
33. Lingala SG, Hu Y, DiBella E, Jacob M,. Accelerated dynamic MRI exploiting sparsity and low-rank structure: k-t SLR. IEEE Trans Med Imag 2011; 30: 1042-1054.
34. Manjon JV, Coupe P, Concha L, Buades A, Collins L, Robles M,. DWI denoising using overcomplete local PCA decomposition. In Proceedings of the 20th Annual Meeting of ISMRM, Melbourne, Australia, 2012. p. 3580.
35. Nguyen HM, Peng X, Do MN, Liang ZP,. Spatiotemporal denoising of MR spectroscopic imaging data by low-rank approximations. In Proceedings of IEEE International Symposium on Biomedical Imaging, 2011. pp. 857-860.
36. Lam F, Babacan SD, Schuff N, Liang ZP,. Denoising diffusion-weighted MR images using low rank structure and edge constraints. In Proceedings of the 20th Annual Meeting of ISMRM, Melbourne, Australia, 2012. p. 4308.
37. Haldar JP, Hernando D,. Rank-constrained solutions to linear matrix equations using powerfactorization. IEEE Signal Process Lett 2009; 16: 584-587.
38. Basser PJ, Jones DK,. Diffusion-tensor MRI: theory, experimental design and data analysis-a technical review. NMR Biomed 2002; 15: 456-467.
39. Yablonskiy DA, Sukstanskii AL,. Theoretical models of the diffusion weighted MR signal. NMR Biomed 2010; 23: 661-681.
40. Santis SD, Gabrielli A, Palombo M, Maraviglia B, Capuani S,. Non-Gaussian diffusion imaging: a brief practical review. Magn Reson Imag 2011; 29: 1410-1416.
41. Tournier J, Mori S, Leemans A,. Diffusion tensor imaging and beyond. Magn Reson Med 2011; 65: 1532-1556.
42. Haldar JP,. Constrained imaging: denoising and sparse sampling. Ph.D. Thesis, University of Illinois at Urbana-Champaign, Urbana, IL, 2011.
43. Nikolava M, Ng MK,. Analysis of half-quadratic minimization methods for signal and image recovery. SIAM J Sci Comput 2005; 27: 937-966.
44. Huber PJ,. Robust statistics. Hoboken, NJ: John Wiley & Sons, 1981.
45. Zhao B, Haldar JP, Brinegar C, Liang ZP,. Low rank matrix recovery for real-time cardiac MRI. In Proceedings of IEEE International Symposium on Biomedical Imaging 2010. pp. 996-999.
46. Nocedal J, Wright SJ,. Numerical optimization. New York: Springer, 2006.
47. Koay CG, Chang LC, Carew JD, Pierpaoli C, Basser PJ,. A unifying theoretical and algorithmic framework for least squares methods of estimation in diffusion tensor imaging. J Magn Reson 2006; 182: 115-125.
48. Haldar JP, Sakaie K, Liang ZP,. Resolution and noise properties of linear phase-constrained partial Fourier reconstruction. In Proceedings of the 17th Annual Meeting of ISMRM, Honolulu, Hawaii, USA, 2009. p. 2862.
49. Griswold MA, Jakob PM, Heidemann RM, Nittka M, Jellus V, Wang J, Kiefer B, Haase A,. Generalized autocalibrating partially parallel acquisitions (GRAPPA). Magn Reson Med 2002; 47: 1202-1210.
50. Wedeen VJ, Hagmann P, Tseng WYI, Reese TG, Weisskoff RM,. Mapping complex tissue architecture with diffusion spectrum magnetic resonance imaging. Magn Reson Med 2005; 54: 1377-1386.
51. Tuch DS,. Q-ball imaging. Magn Reson Med 2004; 52: 1358-1372.
52. Arsigny V, Fillard P, Pennec X, Ayache N,. Log-Euclidean metrics for fast and simple calculus on diffusion tensors. Magn Reson Med 2006; 56: 411-421.
53. Chang LC, Rohde GK, Pierpaoli C,. An automatic method for estimating noise-induced signal variance in magnitude-reconstructed magnetic resonance images. In Proceedings of SPIE, 2005. pp. 1136-1142.
54. Koay CG, Ozarslan E, Pierpaoli C,. Probabilistic identification and estimation of noise (PIESNO): a self-consistent approach and its applications in MRI. J Magn Reson 2009; 199: 94-103.
55. Sijbers J, Poot DHJ, Dekker AD, Pintjens W,. Automatic estimation of the noise variance from the histogram of a magnetic resonance image. Phys Med and Biol 2007; 52: 1335-1348.
56. Coupe P, Manjon JV, Gedamu E, Arnold D, Robles M, Collins DL,. Robust Rician noise estimation for MR images. Med Image Anal 2010; 14: 483-493.
57. Rajan J, Poot D, Juntu J, Sijbers J,. Noise measurement from magnitude MRI using local estimates of variance and skewness. Phys Med and Biol 2010; 55: N441-N445.
58. Landman BA, Bazin PL, Smith SA, Prince JL,. Robust estimation of spatially variable noise fields. Magn Reson Med 2009; 62: 500-509.
59. Maximov II, Farrher E, Grinberg F, Shah NJ,. Spatially variable Rician noise in magnetic resonance imaging. Med Image Anal 2012; 16: 536-548.
60. Craven P, Wahba G,. Smoothing noisy data with spline functions. Numer Math 1978; 31: 377-403.
61. Vogel CR,. Computational methods for inverse problems. Philadelphia, PA: SIAM, 2002