Analysis L1/2 Regularization: Iterative Half Thresholding Algorithm for CS-MRI

Abstract

Recently, the L1/2 regularization has shown its great potential to eliminate the bias problems caused by the convex ${L-{1}}$ regularization in many compressive sensing (CS) tasks. CS-based magnetic resonance imaging (CS-MRI) aims at reconstructing a high-resolution image from under-sampled k-space data, which can shorten the imaging time efficiently. Theoretically, the L1/2 regularization-based CS-MRI will reconstruct the MR images with higher quality to investigate and study the potential and feasibility of the L1/2 regularization for the CS-MRI problem. In this paper, we employ the nonconvex L1/2 -norm to exploit the sparsity of the MR images under the tight frame. Then, two novel iterative half thresholding algorithms (IHTAs) for the analysis of the L1/2 regularization are introduced to solve the nonconvex optimization problem, namely, smoothing-IHTA and projected-IHTA. To evaluate the performance of the L1/2 regularization, we conduct our experiments on the real-world MR data using three different popular sampling masks. All experimental results demonstrate that the L1/2 regularization can improve the L1 regularization significantly and show the potential and feasibility for future practical applications.