MR images reconstruction based on TVWL2-L1 model

Compressive sensing (CS) theory, which has been widely used in magnetic resonance (MR) image processing, indicates that a sparse signal can be reconstructed by the optimization programming process from non-adaptive linear projections. Since MR Images commonly possess a blocky structure and have sparse representations under certain wavelet bases, total variation (TV) and wavelet domain @?"1 norm regularization are enforced together (TV-wavelet L1 method) to improve the recovery accuracy. However, the components of wavelet coefficients are different: low-frequency components of an image, that carry the main energy of the MR image, perform a decisive impact for reconstruction quality. In this paper, we propose a TV and wavelet L2-L1 model (TVWL2-L1) to measure the low frequency wavelet coefficients with @?"2 norm and high frequency wavelet coefficients with @?"1 norm. We present two methods to approach this problem by operator splitting algorithm and proximal gradient algorithm. Experimental results demonstrate that our method can obviously improve the quality of MR image recovery comparing with the original TV-wavelet method.

[1]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[2]  M. Lustig,et al.  Compressed Sensing MRI , 2008, IEEE Signal Processing Magazine.

[3]  David L. Donoho,et al.  Sparse Solution Of Underdetermined Linear Equations By Stagewise Orthogonal Matching Pursuit , 2006 .

[4]  D. Donoho,et al.  Sparse MRI: The application of compressed sensing for rapid MR imaging , 2007, Magnetic resonance in medicine.

[5]  Jean-Luc Starck,et al.  Sparse Solution of Underdetermined Systems of Linear Equations by Stagewise Orthogonal Matching Pursuit , 2012, IEEE Transactions on Information Theory.

[6]  Shiqian Ma,et al.  Fast Multiple-Splitting Algorithms for Convex Optimization , 2009, SIAM J. Optim..

[7]  Shiqian Ma,et al.  An efficient algorithm for compressed MR imaging using total variation and wavelets , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[8]  Junzhou Huang,et al.  Efficient MR image reconstruction for compressed MR imaging , 2011, Medical Image Anal..

[9]  M. A. Iwen.  Simple deterministically constructible RIP matrices with sublinear fourier sampling requirements , 2009, 2009 43rd Annual Conference on Information Sciences and Systems.

[10]  E. Candès,et al.  Sparsity and incoherence in compressive sampling , 2006, math/0611957.

[11]  J. Romberg,et al.  Imaging via Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[12]  E. Candès,et al.  Stable signal recovery from incomplete and inaccurate measurements , 2005, math/0503066.

[13]  I. Daubechies,et al.  An iterative thresholding algorithm for linear inverse problems with a sparsity constraint , 2003, math/0307152.

[14]  P. Lions,et al.  Splitting Algorithms for the Sum of Two Nonlinear Operators , 1979 .

[15]  Marc Teboulle,et al.  A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems , 2009, SIAM J. Imaging Sci..

[16]  Junfeng Yang,et al.  A Fast Alternating Direction Method for TVL1-L2 Signal Reconstruction From Partial Fourier Data , 2010, IEEE Journal of Selected Topics in Signal Processing.

[17]  Benar Fux Svaiter,et al.  General Projective Splitting Methods for Sums of Maximal Monotone Operators , 2009, SIAM J. Control. Optim..

[18]  Boris Polyak,et al.  The method of projections for finding the common point of convex sets , 1967 .

[19]  Marc Teboulle,et al.  Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems , 2009, IEEE Transactions on Image Processing.

[20]  Mário A. T. Figueiredo,et al.  Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems , 2007, IEEE Journal of Selected Topics in Signal Processing.