RNLp: Mixing Nonlocal and TV-Lp Methods to Remove Impulse Noise from Images

Abstract

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 data term and a total variation regularization term. The nonlocal L p term is a weighted L p 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.

Fractional-order diffusion coupled with integer-order diffusion for multiplicative noise removal

“…In order to make nonlocal methods perform well across the entire image, there are currently two approaches. The first approach is to combine local and nonlocal methods, as shown in [33][34][35][36]. The other approach is letting s be spatially dependent in the fractional-order operator.…”

A Convex Variational Model for Learning Convolutional Image Atoms from Incomplete Data

“…Data-adaptive methods such as patch-based methods (see for instance [28,17,11,18]) on the other hand are able to exploit redundant structures in images independent of an a-priory description and are, at least for some specific tasks, often superior to variational-and PDE-based methods. In particular machine-learning-based methods have advanced the state-of-the art significantly in many typical imaging applications in the past years.…”