Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
General Projective Splitting Methods for Sums of Maximal Monotone Operators
SIAM Journal on Control and Optimization
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
IEEE Transactions on Image Processing
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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.