Sparse Regularization Based on Reverse Ordered Weighted L1-Norm and Its Application to Edge-Preserving Smoothing

Sparse regularization is being applied to solve indeterminate inverse problems. However, current regularization is unable to manage sparsity and small perturbations at the same time, and does not perform well enough for some applications. In this study, we propose reversed ordered weighted L1-norm regularization (ROWL) that can tolerate small perturbations while well-handling sparsity. Since ROWL can make proximity mapping easy to compute, it is possible to construct an algorithm to find a suboptimal solution to the inverse problem using the proximity splitting method. Using ROWL for image edge-preserving smoothing, allows us to control both edge sharpness and gradation smoothness.