Limited-angle cone-beam computed tomography image reconstruction by total variation minimization and piecewise-constant modification

Abstract. Because of x-ray dose considerations or practical mechanical restrictions, it may be interesting for some applications to perform limited-angle scanning. So the limited-angle problem is of practical significance in computed tomography (CT). Furthermore, it is an ill-posed problem. Total variation minimization (TVM) and projection on convex sets (POCS) based iterative reconstruction algorithm is comparatively valid for this undersampling CT reconstruction problem and can obtain comparatively good performance. But the reconstruction images have artifacts with gradual change gray nearby edges. In this paper, a simple but efficient method to eliminate such artifacts during the reconstruction is proposed. Based on the same assumption of the TVM algorithm, for the object whose density distribution is approximate piecewise-constant, we develop and investigate an improved iterative reconstruction algorithm for volume image reconstruction from limited-angle cone-beam scan, which is referred to as piecewise-constant modification TVM-POCS (PM-TVM-POCS) algorithm. The grays of voxels with gradually changed gray artifacts are modified in the TVM-POCS iteration process by the piecewise-constant modification algorithm which is regarded as a “collapse” process, and gradually approaches the true piecewise-constant image. The results of simulation experiments show that the presented modification algorithm can improve the quality of the reconstructed image obviously and it is steady to noise. This modification algorithm can also be applied to other reconstruction problems which have artifacts with gradual change gray.