A Primal–Dual Fixed-Point Algorithm for TVL1 Wavelet Inpainting Based on Moreau Envelope

In this paper, we present a novel variational wavelet inpainting based on the total variation (TV) regularization and the l1-norm fitting term. The goal of this model is to recover incomplete wavelet coefficients in the presence of impulsive noise. By incorporating the Moreau envelope, the proposed...

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Dettagli Bibliografici
Autori principali: Zemin Ren, Qifeng Zhang, Yuxing Yuan
Natura: Articolo
Lingua:English
Pubblicazione: MDPI AG 2022-07-01
Serie:Mathematics
Soggetti:
Accesso online:https://www.mdpi.com/2227-7390/10/14/2470
Descrizione
Riassunto:In this paper, we present a novel variational wavelet inpainting based on the total variation (TV) regularization and the l1-norm fitting term. The goal of this model is to recover incomplete wavelet coefficients in the presence of impulsive noise. By incorporating the Moreau envelope, the proposed model for wavelet inpainting can better handle the non-differentiability of the l1-norm fitting term. A modified primal dual fixed-point algorithm is developed based on the proximity operator to solve the proposed variational model. Moreover, we consider the existence of solution for the proposed model and the convergence analysis of the developed iterative scheme in this paper. Numerical experiments show the desirable performance of our method.
ISSN:2227-7390