A Regularized Limited-Angle CT Reconstruction Model Based on Sparse Multi-level Information Groups of the Images

Restricted by the scanning environment and the shape of the target to be detected, the obtained projection data from computed tomography (CT) are usually incomplete, which leads to a seriously ill-posed problem, such as limited-angle CT reconstruction. In this situation, the classical filtered back-projection (FBP) algorithm loses efficacy especially when the scanning angle is seriously limited. By comparison, the simultaneous algebraic reconstruction technique (SART) can deal with the noise better than FBP, but it is also interfered by the limited-angle artifacts. At the same time, the total variation (TV) algorithm has the ability to address the limited-angle artifacts, since it takes into account a priori information about the target to be reconstructed, which alleviates the ill-posedness of the problem. Nonetheless, the current algorithms exist limitations when dealing with the limited-angle CT reconstruction problem. This paper analyses the distribution of the limited-angle artifacts, and it emerges globally. Then, motivated by TV algorithm, tight frame wavelet decomposition and group sparsity, this paper presents a regularization model based on sparse multi-level information groups of the images to address the limited-angle CT reconstruction, and the corresponding algorithm called modified proximal alternating linearized minimization (MPALM) is presented to deal with the proposed model. Numerical implementations demonstrate the effectiveness of the presented algorithms compared with the above classical algorithms.