Analysis ${{L_{{1/2}}}}$ Regularization: Iterative Half Thresholding Algorithm for CS-MRI

Recently, the L
_1/2
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 L
_1/2
regularization-based CS-MRI will reconstruct the MR images with higher quality to investigate and study the potential and feasibility of the L
_1/2
regularization for the CS-MRI problem. In this paper, we employ the nonconvex L
_1/2
-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 L
_1/2
regularization are introduced to solve the nonconvex optimization problem, namely, smoothing-IHTA and projected-IHTA. To evaluate the performance of the L
_1/2
regularization, we conduct our experiments on the real-world MR data using three different popular sampling masks. All experimental results demonstrate that the L
_1/2
regularization can improve the L
₁
regularization significantly and show the potential and feasibility for future practical applications.