Edge-preserving reconstruction with contour-line smoothing and non-quadratic data-fidelity

Abstract

The standard approach for image reconstruction is to stabilize the problem by including an edge-preserving roughness penalty in addition to faithfulness to the data. However, this methodology produces noisy object boundaries and creates a staircase effect. State-of-the-art methods to correct these undesirable effects either have weak convergence guarantees or are limited to specific situations; furthermore, most of them use a quadratic data-fidelity term. In this paper, we propose a simple alternative regularization model to improve contour regularity and to reduce the staircase effect-our model incorporates the smoothness of the edge field in an implicit way by adding a simple penalty term defined in the wavelet domain. We also derive an efficient half-quadratic algorithm to solve the resulting optimization problem, including the case when the data-fidelity term is not quadratic and the cost function is not convex. Our approach either extends or supplements existing methods and offers strong convergence guarantees. Numerical experiments show that it outperforms first-order total variation regularization as well as state-of-the-art second-order regularization techniques.