Wavelet inpainting with the \(\ell_{0}\) sparse regularization

DOI10.1016/j.acha.2015.03.001zbMath1338.65061OpenAlexW2021603736MaRDI QIDQ285527

Yuesheng Xu, Xueying Zeng, Li-Xin Shen

Publication date: 19 May 2016

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.acha.2015.03.001

zbMATH Keywords

waveletnumerical experimentimage reconstructiondiscrete cosine transformimage inpainting\(\ell_0\) normfixed-point proximity algorithmframelet systemMoreau envelopesparse regularizationtight frame

Mathematics Subject Classification ID

Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Numerical methods for wavelets (65T60) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Numerical methods for discrete and fast Fourier transforms (65T50)

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Cites Work

• Unnamed Item
• A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
• Fast total variation wavelet inpainting via approximated primal-dual hybrid gradient algorithm
• Proximal alternating linearized minimization for nonconvex and nonsmooth problems
• A unified primal-dual algorithm framework based on Bregman iteration
• Total variation wavelet inpainting
• Fast Fourier transforms: A tutorial review and a state of the art
• Wavelet inpainting by nonlocal total variation
• A first-order primal-dual algorithm for convex problems with applications to imaging
• Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss-Seidel methods
• Proximity algorithms for the L1/TV image denoising model
• The Moreau envelope approach for the L1/TV image denoising model
• A framelet-based image inpainting algorithm
• Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA)
• Mathematical Models for Local Nontexture Inpaintings
• Proximity algorithms for image models: denoising
• Alternating Direction Method for Image Inpainting in Wavelet Domains
• Preconditioned alternating projection algorithms for maximum a posteriori ECT reconstruction
• A proximity algorithm accelerated by Gauss–Seidel iterations for L1/TV denoising models
• Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality
• Fixed-Point Continuation for $\ell_1$-Minimization: Methodology and Convergence
• Image decomposition via the combination of sparse representations and a variational approach
• Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
• From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
• Ten Lectures on Wavelets
• Variational Analysis
• Wavelet Algorithms for High-Resolution Image Reconstruction
• Euler's Elastica and Curvature-Based Inpainting
• $\ell _0$ Minimization for wavelet frame based image restoration
• A primal–dual fixed point algorithm for convex separable minimization with applications to image restoration
• A Fast Optimization Transfer Algorithm for Image Inpainting in Wavelet Domains
• Framelet Algorithms for De-Blurring Images Corrupted by Impulse Plus Gaussian Noise
• A Primal–Dual Method for Total-Variation-Based Wavelet Domain Inpainting
• Adaptive Inpainting Algorithm Based on DCT Induced Wavelet Regularization
• Signal Recovery by Proximal Forward-Backward Splitting
• An Iterative Regularization Method for Total Variation-Based Image Restoration
• Compressed sensing

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