Adaptive Weighted Total Variation Minimization Based Alternating Direction Method of Multipliers for Limited Angle CT Reconstruction

Abstract

In CT image reconstruction, the limited angle problem is an ill-posed problem. To solve this ill-posed problem, the total variation (TV) regularization has been widely used in image reconstruction. In recent years, an algorithm based on TV regularization and alternating direction multiplier method has been proposed and named as ADTVM. ADTVM can reconstruct high-quality images for the limited angle problem. However, ADTVM just considers the homogeneity of image at different directions. In real application, image possesses different properties at different directions. Therefore, we construct an adaptive weighted TV (AwTV) regularization and propose the ADM-AwTV method on the basis of ADTVM. ADM-AwTV is an iterative image reconstruction method which can reveal the anisotropy of image, adaptively. In each iteration, the weights of different directions can update according to the last reconstruction image. Experiments on two simulation images and one real projection data show that the proposed method achieves better reconstruction results than the other iterative image reconstruction methods such as ART-TV and ADTVM for the limited angle problem.