A Visually Better Recovered Image Selection for Imaging Inverse Problems

摘要

In the last decade, many image recovery problems have been formulated as a certain nonsmooth convex minimization problem (we call it an original problem), and its minimizer, i.e., a recovery image, is not unique in some cases. In such cases, there exists visually different recovery images, and conventional image recovery techniques can not select a desired (visually better) recovery image. In this paper, we propose an optimization framework which allows us to select a better recovery image of the original problem in terms of the visual quality. First, a criteria function is introduced to choose a visually better recovery image from the set of minimizers of the original problem. Then, we formulate a hierarchical convex optimization problem which minimizes the criteria function over the set. The iterative algorithm based on the hybrid steepest descent method to solve the problem is also presented. To apply the hybrid steepest descent method to the problem, we characterize the set of the minimizers of the original problem by the Douglas-Rachford splitting operator. Numerical results showed that, in case of the total variation based recovery, a visually better recovery image can be obtained by using our method.