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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Veröffentlicht in:Mathematics (Basel) Jg. 10; H. 14; S. 2470
Hauptverfasser: Ren, Zemin, Zhang, Qifeng, Yuan, Yuxing
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Basel MDPI AG 01.07.2022
Schlagworte:
Algorithms
fixed point algorithm
impulsive noise
Iterative methods
Mathematics
Methods
Moreau envelope
Partial differential equations
proximity operator
Regularization
wavelet inpainting
Wavelet transforms
ISSN:2227-7390, 2227-7390
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
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content type line 14
ISSN:2227-7390
2227-7390
DOI:10.3390/math10142470