LAUSR

We propose a new variational framework to remove random-valued impulse noise from images. This framework combines, in the same energy, a nonlocal $$L^p$$Lp data term and a total variation regularization term. The nonlocal $$L^p$$Lp term is a weighted $$L^p$$Lp distance between pixels, where the weights depend on a robust distance between patches centered at the pixels. In a first part, we study the theoretical properties of the proposed energy, and we show how it is related to classical denoising models for extreme choices of the parameters. In a second part, after having explained how to numerically find a minimizer of the energy thanks to primal-dual approaches, we show extensive denoising experiments on various images and noise intensities. The denoising performance of the proposed methods is on par with state-of-the-art approaches, and the remarkable fact is that, unlike other successful variational approaches for impulse noise removal, they do not rely on a noise detector.