$\ell _0$ Minimization for wavelet frame based image restoration

DOI10.1090/S0025-5718-2012-02631-7zbMath1277.80022OpenAlexW2963347434WikidataQ113091015 ScholiaQ113091015MaRDI QIDQ4912013

Bin Dong, Zhaosong Lu, Yong Zhang

Publication date: 20 March 2013

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-2012-02631-7

zbMATH Keywords

image restorationwavelet framehard thresholding\(l_0\) minimization

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Nonconvex programming, global optimization (90C26) Computing methodologies for image processing (68U10) Optimization problems in thermodynamics and heat transfer (80M50)

Related Items

Exact penalization for cardinality and rank-constrained optimization problems via partial regularization, Wavelet frame based image restoration via combined sparsity and nonlocal prior of coefficients, Wavelet inpainting with the \(\ell_{0}\) sparse regularization, Adaptive frame-based color image denoising, Image restoration: a wavelet frame based model for piecewise smooth functions and beyond, A General Non-Lipschitz Infimal Convolution Regularized Model: Lower Bound Theory and Algorithm, Error bounds and stability in the \(\ell_0\) regularized for CT reconstruction from small projections, CT Image Reconstruction by Spatial-Radon Domain Data-Driven Tight Frame Regularization, A wavelet frame constrained total generalized variation model for imaging conductivity distribution, Convergence and stability analysis of the half thresholding based few-view CT reconstruction, A general selective averaging method for piecewise constant signal and image processing, Existence and convergence analysis of \(\ell_{0}\) and \(\ell_{2}\) regularizations for limited-angle CT reconstruction, Wavelet tight frame and prior image-based image reconstruction from limited-angle projection data, On the local and global minimizers of $ \newcommand{\e}{{\rm e}} \ell_0$ gradient regularized model with box constraints for image restoration, Topology optimization for inverse magnetostatics as sparse regression: application to electromagnetic coils for stellarators, A cascading l0 regularization reconstruction method in nonsubsampled contourlet domain for limited-angle CT, A nonconvex truncated regularization and box-constrained model for CT reconstruction, Disparity and optical flow partitioning using extended Potts priors, $ \newcommand{\e}{{\rm e}} \ell_{0}$ -minimization methods for image restoration problems based on wavelet frames, Zero norm based analysis model for image smoothing and reconstruction, CURE: Curvature Regularization for Missing Data Recovery, An adaptive iteration reconstruction method for limited-angle CT image reconstruction, A non-smooth and non-convex regularization method for limited-angle CT image reconstruction, Image Restoration: Wavelet Frame Shrinkage, Nonlinear Evolution PDEs, and Beyond, Data-driven tight frame learning scheme based on local and non-local sparsity with application to image recovery, Capped \(\ell_p\) approximations for the composite \(\ell_0\) regularization problem, A Reweighted Joint Spatial-Radon Domain CT Image Reconstruction Model for Metal Artifact Reduction, PCM-TV-TFV: A Novel Two-Stage Framework for Image Reconstruction from Fourier Data, The proximal alternating iterative hard thresholding method for \(l_0\) minimization, with complexity \(\mathcal{O}(1/\sqrt{k})\), Iterative Potts minimization for the recovery of signals with discontinuities from indirect measurements: the multivariate case, Guided image filtering based \(\ell_0\) gradient minimization for limited-angle CT image reconstruction, An edge driven wavelet frame model for image restoration, Sparsity promoting regularization for effective noise suppression in SPECT image reconstruction, A variational proximal alternating linearized minimization in a given metric for limited-angle CT image reconstruction, A new proximal iterative hard thresholding method with extrapolation for \(\ell _0\) minimization, Alternating method based on framelet l₀-norm and TV regularization for image restoration, On a general smoothly truncated regularization for variational piecewise constant image restoration: construction and convergent algorithms, A stochastic alternating direction method of multipliers for non-smooth and non-convex optimization, A note on the complexity of proximal iterative hard thresholding algorithm

Uses Software

• RecPF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlinear total variation based noise removal algorithms
• A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
• Compressed sensing with coherent and redundant dictionaries
• Frame based segmentation for medical images
• Simultaneous cartoon and texture inpainting
• Wavelet frame based surface reconstruction from unorganized points
• Iterative hard thresholding for compressed sensing
• Iterative thresholding for sparse approximations
• Iteratively solving linear inverse problems under general convex constraints
• Image recovery via total variation minimization and related problems
• Affine systems in \(L_ 2(\mathbb{R}^d)\): The analysis of the analysis operator
• Tight frame: an efficient way for high-resolution image reconstruction
• Level set methods and dynamic implicit surfaces
• Framelets: MRA-based constructions of wavelet frames
• Deconvolution: a wavelet frame approach
• A framelet algorithm for enhancing video stills
• Convergence analysis of tight framelet approach for missing data recovery
• A framelet-based image inpainting algorithm
• Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA)
• An Accelerated Proximal Gradient Algorithm for Frame-Based Image Restoration via the Balanced Approach
• A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
• Linearized Bregman Iterations for Frame-Based Image Deblurring
• The Split Bregman Method for L1-Regularized Problems
• An EM algorithm for wavelet-based image restoration
• Image decomposition via the combination of sparse representations and a variational approach
• Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
• Decoding by Linear Programming
• Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
• Split Bregman Methods and Frame Based Image Restoration
• Ten Lectures on Wavelets
• Variational Analysis
• Wavelet Algorithms for High-Resolution Image Reconstruction
• Regularization of Wavelet Approximations
• Nonmonotone Spectral Projected Gradient Methods on Convex Sets
• On the Equivalence of Soft Wavelet Shrinkage, Total Variation Diffusion, Total Variation Regularization, and SIDEs
• Image restoration: Total variation, wavelet frames, and beyond
• Image Processing and Analysis
• Compressed sensing
• Convergence of a block coordinate descent method for nondifferentiable minimization