Spatial-Frequency Domain Nonlocal Total Variation for Image Denoising

TL;DR

This paper introduces a novel image denoising method combining total variation and non-local means in both spatial and Fourier domains, achieving superior quality and speed.

Contribution

It proposes the L-SFNLTV model that applies denoising in space and Fourier domains and introduces a local, regionwise implementation with aggregation.

Findings

L-SFNLTV outperforms recent NLTV-based methods in image quality.

L-SFNLTV offers faster computational speed.

The method effectively exploits spatial and frequency domain complementarity.

Abstract

Following the pioneering works of Rudin, Osher and Fatemi on total variation (TV) and of Buades, Coll and Morel on non-local means (NL-means), the last decade has seen a large number of denoising methods mixing these two approaches, starting with the nonlocal total variation (NLTV) model. The present article proposes an analysis of the NLTV model for image denoising as well as a number of improvements, the most important of which being to apply the denoising both in the space domain and in the Fourier domain, in order to exploit the complementarity of the representation of image data in both domains. A local version obtained by a regionwise implementation followed by an aggregation process, called Local Spatial-Frequency NLTV (L- SFNLTV) model, is finally proposed as a new reference algorithm for image denoising among the family of approaches mixing TV and NL operators. The experiments show the great performance of L-SFNLTV, both in terms of image quality and of computational speed, comparing with other recently proposed NLTV-related methods.