Reweighted Anisotropic Total Variation Minimization for Limited-Angle CT Reconstruction

Abstract

Limited-angle problems encountered in computed tomography (CT) often necessitate image reconstruction using projection data from a particular angle range. To solve this severely ill-posed problem, prior information is utilized to constrain the problem. As a special case of compressed sensing, a total variation (TV) transform with an $l_{1}$ -norm image gradient is utilized in most cases, and manages to obtain very impressive reconstruction results. However, it is unfit for limited-angle problems owing to its isotropic property. This paper proposes a new iteratively reweighted anisotropic TV (ATV) method, in which a reweighted technique is incorporated into the idea of ATV. Our strategy successfully combines their merits and results in significantly improved performance. By using the reweighted technique, we are able to approximate the most direct measure of sparsity— $l_{0}$ -norm—better than $l_{1}$ -norm. As a result, the property of image sparsity can be utilized more efficiently. Because TV is isotropic, which prevents detection of blurred edges caused by missing angle ranges and may weaken edge-preserving ability along nonblurred directions, we consider the angle range of the data as additional prior information by assigning different weights to different directions; this allows the anisotropic property to be utilized. Therefore, the blurred directions can be prevented from affecting edge detection, and better reconstruction results can be achieved. To demonstrate the advantages of our method, we perform reconstruction using projection data from phantom CT scans and actual CT scans. We conducted comprehensive comparison between our method and many existing TV-based methods. Both qualitative and quantitative results are presented.