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

Zemin Ren, Qifeng Zhang and Yuxing Yuan
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Zemin Ren: School of Mathematics and Physics, Chongqing University of Science and Technology, Chongqing 401331, China
Qifeng Zhang: College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
Yuxing Yuan: School of Mathematics and Physics, Chongqing University of Science and Technology, Chongqing 401331, China

Mathematics, 2022, vol. 10, issue 14, 1-13

Abstract: 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.

Keywords: wavelet inpainting; Moreau envelope; proximity operator; fixed point algorithm; impulsive noise (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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