Spatial-Frequency domain nonlocal total variation for image denoising

Haijuan Hu (1) , Jacques Froment (2) , Baoyan Wang (3) , Xiequan Fan (4)

1 Northeastern University at Qinhuangdao
2 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique
3 Guangdong University of Petrochemical Technology
4 TJU - Tianjin University

Following the pioneering works of Rudin, Osher and Fatemi on total variation (TV) and of Buades, Coll and Morel on non-local means (NLmeans), 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. 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 in terms of image quality and of computational speed, comparing with other recently proposed NLTV-related methods.

Mots clés: Nonlocal total variation; Discrete Fourier transform; Image denoising; SURE; Regionwise implementation

Domaines: Traitement du signal et de l'image [eess.SP]

Haijuan Hu, Jacques Froment, Baoyan Wang, Xiequan Fan. Spatial-Frequency domain nonlocal total variation for image denoising. Inverse Problems and Imaging , 2020, 14 (6), pp.1157-1184. ⟨10.3934/ipi.2020059⟩. ⟨hal-03146469⟩