Variational image denoising with adaptive constraint sets

Abstract. We propose a generalization of the total variation (TV) minimization method proposed by Rudin, Osher and Fatemi. This generalization allows for adaptive regularization, which depends on the minimizer itself. Existence theory is provided in the framework of quasi-variational inequalities. We demonstrate the usability of our approach by considering applications for image and movie denoising

Solving Adaptive Image Restoration Problems via a Modified Projection Algorithm

We introduce a new general TV regularizer, namely, generalized TV regularization, to study image denoising and nonblind image deblurring problems. In order to discuss the generalized TV image restoration with solution-driven adaptivity, we consider the existence and uniqueness of the solution for mixed quasi-variational inequality. Moreover, the convergence of a modified projection algorithm for solving mixed quasi-variational inequalities is also shown. The corresponding experimental results support our theoretical findings