Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Mathematical Programming: Series A and B
Iterative methods for total variation denoising
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Recovery of blocky images from noisy and blurred data
SIAM Journal on Applied Mathematics
A Fast Algorithm for Deblurring Models with Neumann Boundary Conditions
SIAM Journal on Scientific Computing
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Wavelets and curvelets for image deconvolution: a combined approach
Signal Processing - Special section: Security of data hiding technologies
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Total Variation Wavelet Inpainting
Journal of Mathematical Imaging and Vision
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programming
Mathematical Programming: Series A and B
Split Bregman Algorithm, Douglas-Rachford Splitting and Frame Shrinkage
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
An Efficient TVL1 Algorithm for Deblurring Multichannel Images Corrupted by Impulsive Noise
SIAM Journal on Scientific Computing
A fast optimization transfer algorithm for image inpainting in wavelet domains
IEEE Transactions on Image Processing
The Split Bregman Method for L1-Regularized Problems
SIAM Journal on Imaging Sciences
A Fast Algorithm for Edge-Preserving Variational Multichannel Image Restoration
SIAM Journal on Imaging Sciences
A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
SIAM Journal on Imaging Sciences
Fast image recovery using variable splitting and constrained optimization
IEEE Transactions on Image Processing
SIAM Journal on Scientific Computing
Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction
SIAM Journal on Imaging Sciences
A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging
Journal of Mathematical Imaging and Vision
Alternating Direction Algorithms for $\ell_1$-Problems in Compressive Sensing
SIAM Journal on Scientific Computing
Recovering Low-Rank and Sparse Components of Matrices from Incomplete and Noisy Observations
SIAM Journal on Optimization
Why Simple Shrinkage Is Still Relevant for Redundant Representations?
IEEE Transactions on Information Theory
Fast, robust total variation-based reconstruction of noisy, blurred images
IEEE Transactions on Image Processing
Filling-in by joint interpolation of vector fields and gray levels
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
An EM algorithm for wavelet-based image restoration
IEEE Transactions on Image Processing
A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration
IEEE Transactions on Image Processing
Nonlinear image recovery with half-quadratic regularization
IEEE Transactions on Image Processing
Inexact Alternating Direction Methods for Image Recovery
SIAM Journal on Scientific Computing
On the $O(1/n)$ Convergence Rate of the Douglas-Rachford Alternating Direction Method
SIAM Journal on Numerical Analysis
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Image inpainting in wavelet domains refers to the recovery of an image from incomplete and/or inaccurate wavelet coefficients. To reconstruct the image, total variation (TV) models have been widely used in the literature, and they produce high-quality reconstructed images. In this paper, we consider an unconstrained, TV-regularized, $\ell_2$-data-fitting model to recover the image. The model is solved by the alternating direction method (ADM). At each iteration, the ADM needs to solve three subproblems, all of which have closed-form solutions. The per-iteration computational cost of the ADM is dominated by two Fourier transforms and two wavelet transforms, all of which admit fast computation. Convergence of the ADM iterative scheme is readily obtained. We also discuss extensions of this ADM scheme to solving two closely related constrained models. We present numerical results to show the efficiency and stability of the ADM for solving wavelet domain image inpainting problems. Numerical results comparing the ADM with some recent algorithms are also reported.