l_1/2 regularization for wavelet frames based few-view CT reconstruction

¹ Chongqing Key Laboratory of Complex Data Analysis & Artificial Intelligence, Chongqing University of Arts and Sciences, Chongqing, 402160, China
² Chongqing Key Laboratory of Group & Graph Theories and Applications, Chongqing University of Arts and Sciences, Chongqing, 402160, China
³ Chongqing College of Electronic Engineering, Department of Physical Education and Defense Education, Chongqing, 401331, China
⁴ Key Lab for OCME, School of Mathematical Sciences, Chongqing Normal University, Chongqing, 400047, China
⁵ Engineering Research Center of Industrial Computed Tomography Nondestructive Testing of the Education Ministry of China, Chongqing University, Chongqing, 400044, China

^* Corresponding author: linglizhang@cqwu.edu.cn

Abstract

Reducing the radiation exposure in computed tomography (CT) is always a significant research topic in radiology. Image reconstruction from few-view projection is a reasonable and effective way to decrease the number of rays to lower the radiation exposure. But how to maintain high image reconstruction quality while reducing radiation exposure is a major challenge. To solve this problem, several researchers are absorbed in l₀ or l₁ regularization based optimization models to deal with it. However, the solution of l₁ regularization based optimization model is not sparser than that of l_1/2 or l₀ regularization, and solving the l₀ regularization is more difficult than solving the l_1/2 regularization. In this paper, we develop l_1/2 regularization for wavelet frames based image reconstruction model to research the few-view problem. First, the existence of the solution of the corresponding model is demonstrated. Second, an alternate direction method (ADM) is utilized to separate the original problem into two subproblems, where the former subproblem about the image is solved using the idea of the proximal mapping, the simultaneous algebraic reconstruction technique (SART) and the projection and contraction (PC) algorithm, and the later subproblem about the wavelet coefficients is solved using the half thresholding (HT) algorithm. Furthermore, the convergence analysis of our method is given by the simulated implementions. Simulated and real experiments confirm the effectiveness of our method.