Bayesian Regulators to Promote Sharp Image Edges in Limited-Angle Tomography by Combining L 1 and L 2 norms.

Abstract

When the image reconstruction problem is severely ill-conditioned, for example, when the scanning angle is small, the analytic reconstruction algorithms produce images with too many artifacts to be useful in practice, while iterative Bayesian reconstruction algorithms can produce better images. The main purpose of Bayesian constraints is to regulate and stabilize the algorithm. Bayesian penalty minimization is a popular and effective method in regulating, denoising, and edge preserving. The main players for the Bayesian regulators are the total-variation (TV), Huber, $L_0,L_1,L_2$ , and $L_q$ norms. This paper suggests some other methods to regulate an iterative algorithm and to encourage sharp image edges. Some computer simulations are provided. The $L_q$ -like regulators seem to be more effective than Huber regulators in terms of edge-preserving. In this paper, we propose the combination of the user-friendly $L_1$ and $L_2$ norms to approximate the user-unfriendly $L_q$ norm.