An image reconstruction model regularized by edge-preserving diffusion and smoothing for limited-angle computed tomography

Abstract

Limited-angle computed tomography is a very challenging problem in applications. Due to a high degree of ill-posedness, conventional reconstruction algorithms will introduce blurring along the directions perpendicular to the missing projection lines, as well as streak artifacts when applied on limited-angle data. Various models and algorithms have been proposed to improve the reconstruction quality by incorporating priors, among which the total variation, i.e. l1 norm of gradient, and l0 norm of the gradient are the most popular ones. These models and algorithms partially solve the blurring problem under certain situations. However, the fundamental difficulty remains. In this paper, we propose a reconstruction model for limited-angle computed tomography, which incorporates two regularization terms that play the role of edge-preserving diffusion and smoothing along the x-direction and y -direction respectively. Then, an alternating minimization algorithm is proposed to solve the model approximately. The proposed model is inspired by the theory of visible and invisible singularities of limited-angle data, developed by Quinto et al. By incorporating visible singularities as priors into an iterative procedure, the proposed algorithm could produce promising results and outperforms state-of-the-art algorithms for certain limited-angle computed tomography applications. Extensive experiments on both simulated data and real data are provided to validate our model and algorithm.