Sparse-view image reconstruction with nonlocal total variation

The concept of computed tomography (CT) reconstruction from sparse-view data has been a considerable area of much research over the last several years. With the famous piecewise constant assumption, total variation (TV) model has been shown that it could be successfully applied to sparse-view CT reconstruction for producing accurate reconstructions. However, the resulting images from the traditional TV model based on local operators always meet the problems of smeared edges or staircase effects. In this paper, the TV minimization reconstruction model is extanded to a nonlocal TV (NLTV) model, using auxiliary variables and efficient split Bregman iterartive scheme, a reconstruction algorithm based on NLTV minimization has been developed. The proposed method shows excellent properties of edge preserving and smoothness preserving by using the nonlocal operators. Experimental results indicate that the proposed method could solve the above mentioned effects and reconstruct more accurate than the popular split Bregman-TV algorithm when applied to a sparse-view problem.