A New Method for Evaluation of Random Undersampling Matrix in Compressed Sensing-MRI

doi:10.11938/cjmr20150404

Abstract

Abstract:

In compressed sensing magnetic resonance imaging (CS-MRI), the quality of reconstructed image is largely determined by the random undersampling matrix. It is a common practice to select the random undersampling matrix though computation of the point spread function (PSF) and the maximal artifacts possible. In this paper, we proposed to use two novel statistical parameters, mean value (MV) and standard deviation (SD), to guide the selection of random undersampling matrix. The two parameters evaluate the average amplitude and fluctuation of the possible artifacts, respectively. Experiments on mice brain and human brain were used to compare image quality of CS reconstructions of MRI data acquired with random undersampling matrices determined by different criteria. It was shown that reconstruction with MV had better performance when the sampling ratio is above four times of sparsity. It is concluded that better CS-MRI reconstruction quality can be achieved with reasonable selection of sampling ratio guided by prior knowledge of sparsity and MV as random undersampling matrix evaluation parameter.

Key words: MRI, compressed sensing, random undersampling matrix, point spread function

CLC Number:

O482.53

XIAO Sa1,2， LV Zhi-cheng1， SUN Xian-ping1， YE Chao-hui1， ZHOU Xin1*. A New Method for Evaluation of Random Undersampling Matrix in Compressed Sensing-MRI
[J]. Chinese Journal of Magnetic Resonance, 2015, 32(4): 584-595.

References

[1] Candes E J, Romberg J K, Tao T. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information[J]. IEEE T Inform Theory, 2006, 52(2): 489－509.

[2] Donoho D L. Compressed sensing[J]. IEEE T Inform Theory, 2006, 52(4): 1 289－1 306.

[3] Candes E J, Tao T. Near-optimal signal recovery from random projections: Universal encoding strategies[J]. IEEE T Inform Theory, 2006, 52(12): 5 406－5 425.

[4] Wech T, Lemke A, Medway D, et al. Accelerating cine-MR imaging in mouse hearts using compressed sensing[J]. J Magn Reson Imaging, 2011, 34(5): 1 072－1 079.

[5] Gao Ming-sheng(高明生), Xie Hai-bin(谢海滨), Yan Xu(严序), et al. Selective dual-direction sequential compressed sensing for dynamic MR imaging(选择性双向顺序压缩感知重建动态磁共振成像)[J]. Chinese J Magn Reson(波谱学杂志), 2013, 30(2): 194－203.

[6] Li Hai-dong(李海东), Zhang Zhi-ying(张智颖), Han Ye-qing(韩叶清), et al. Lung MRI using hyperpolarized gases(超极化气体肺部磁共振成像)[J]. Chinese J Magn Reson(波谱学杂志), 2014, 31(3): 307－320.

[7] Lustig M, Donoho D L, Pauly J M. Sparse MRI: The application of compressed sensing for rapid MR imaging[J]. Magn Reson Med, 2007, 58(6): 1 182－1 195.

[8] Lustig M, Donoho D L, Santos J M, et al. Compressed sensing MRI[J]. IEEE Signal Proc Mag, 2008, 25(2): 72－82.

[9] Ajraoui S, Lee K J, Deppe M H, et al. Compressed sensing in hyperpolarized He-3 lung MRI[J]. Magn Reson Med, 2010, 63(4): 1 059－1 069.

[10] Qu X B, Zhang W R, Guo D, et al. Iterative thresholding compressed sensing MRI based on contourlet transform[J]. Inverse Probl Sci En, 2010, 18(6):737－758.

[11] Ravishankar S, Bresler Y. MR image reconstruction from highly undersampled k-space data by dictionary learning[J]. IEEE T Med Imaging, 2011, 30(5): 1 028－1 041.

[12] Qu X B, Guo D, Ning B D, et al. Undersampled MRI reconstruction with patch-based directional wavelets[J]. Magn Reson Imaging, 2012, 30(7): 964－977.

[13] Song Y, Zhu Z, Lu Y, et al. Reconstruction of magnetic resonance imaging by three-dimensional dual-dictionary learning[J]. Magn Reson Med, 2014, 71(3): 1 285－1 298.

[14] Qu X B, Hou Y K, Lam F, et al. Magnetic resonance image reconstruction from undersampled measurements using a patch-based nonlocal operator[J]. Med Image Anal, 2014, 18(6): 843－856.

[15] Chen S S B, Donoho D L, Saunders M A. Atomic decomposition by basis pursuit[J]. Siam J Sci Comput, 1998, 20(1): 33－61.

[16] Ye J C, Tak S, Han Y, et al. Projection reconstruction MR imaging using FOCUSS[J]. Magn Reson Med, 2007, 57(4): 764－775.

[17] Donoho D L, Elad M, Temlyakov V N. Stable recovery of sparse overcomplete representations in the presence of noise[J]. IEEE T Inform Theory, 2006, 52(1): 6－18.

[18] Daubechies I, Defrise M, De Mol C. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint[J]. Commun Pur Appl Math, 2004, 57(11): 1 413－1 457.

[19] Starck J L, Elad M, Donoho D L. Image decomposition via the combination of sparse representations and a variational approach[J]. IEEE T Image Process, 2005, 14(10): 1 570－1 582.

[20] Elad M, Matalon B, Zibulevsky M. Coordinate and subspace optimization methods for linear least squares with non-quadratic regularization[J]. Appl Comput Harmon Anal, 2007, 23(3): 346－367.

[21] Kim S J, Koh K, Lustig M, et al. An interior-point method for large-scale l(1)-regularized least squares[J]. IEEE J STSP, 2007, 1(4): 606－617.

[22] Ajraoui S, Parra-Robles J, Wild J M. Incorporation of prior knowledge in compressed sensing for faster acquisition of hyperpolarized gas images[J]. Magn Reson Med, 2013, 69(2): 360－369.

[23] Imai H, Kimura A, Hori Y, et al. Hyperpolarized ¹²⁹Xe lung MRI in spontaneously breathing mice with respiratory gated fast imaging and its application to pulmonary functional imaging[J]. NMR Biomed, 2011, 24(10): 1 343－1 352.

[24] Pang Y, Zhang X. Interpolated compressed sensing for 2D multiple slice fast MR imaging[J]. PLOS ONE, 2013, 8(2): e56098.

[25] Candes E J, Wakin M B. An introduction to compressive sampling[J]. IEEE Signal Proc Mag, 2008, 25(2): 21－30.

[26] Sun Yu-bao(孙玉宝), Wei Zhi-hui(韦志辉), Wu Min(吴敏), et al. Image poisson denoising using sparse representations (稀疏性正则化的图像泊松去噪算法)[J]. Acta Electronica Sinica(电子学报), 2011, 39(2): 285－290.

[27] Fang L, Li S, Nie Q, et al. Sparsity based denoising of spectral domain optical coherence tomography images[J]. Biomedical Opt Express, 2012, 3(5): 927－942.