A Generalized Two-Level Bregman Method with Dictionary Updating for Non-Convex Magnetic Resonance Imaging Reconstruction

doi:10.1007/s12204-015-1674-z

Abstract

Abstract:

In recent years, it has shown that a generalized thresholding algorithm is useful for inverse problems with sparsity constraints. The generalized thresholding minimizes the non-convex $p$ -norm based function with $p < 1$ , and it penalizes small coefficients over a wider range meanwhile applies less bias to the larger coefficients. In this work, on the basis of two-level Bregman method with dictionary updating (TBMDU), we use the modified thresholding to minimize the non-convex function and propose the generalized TBMDU (GTBMDU) algorithm. The experimental results on magnetic resonance (MR) image simulations and real MR data, under a variety of sampling trajectories and acceleration factors, consistently demonstrate that the proposed algorithm can efficiently reconstruct the MR images and present advantages over the previous soft thresholding approaches.

CLC Number:

TN 911.73

Ming-hui ZHANG, Xiao-yang HE, Shen-yuan DU, Qie-gen* LIU. A Generalized Two-Level Bregman Method with Dictionary Updating for Non-Convex Magnetic Resonance Imaging Reconstruction[J]. Journal of Shanghai Jiao Tong University(Science), 2015, 20(6): 660-669.

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