Sparse-view image reconstruction via total absolute curvature combining total variation for X-ray computed tomography

Sparse-view imaging is a promising scanning approach which has fast scanning rate and low-radiation dose in X-ray computed tomography (CT). Conventional L1-norm based total variation (TV) has been widely used in image reconstruction since the advent of compressive sensing theory. However, with only the first order information of the image used, the TV often generates dissatisfactory image for some applications. As is widely known, image curvature is among the most important second order features of images and can potentially be applied in image reconstruction for quality improvement. This study incorporates the curvature in the optimization model and proposes a new total absolute curvature (TAC) based reconstruction method. The proposed model contains both total absolute curvature and total variation (TAC-TV), which are intended for better description of the featured complicated image. As for the practical algorithm development, the efficient alternating direction method of multipliers (ADMM) is utilized, which generates a practical and easy-coded algorithm. The TAC-TV iterations mainly contain FFTs, soft-thresholding and projection operations and can be launched on graphics processing unit, which leads to relatively high performance. To evaluate the presented algorithm, both qualitative and quantitative studies were performed using various few view datasets. The results illustrated that the proposed approach yielded better reconstruction quality and satisfied convergence property compared with TV-based methods.