Some First-Order Algorithms for Total Variation Based Image Restoration
Journal of Mathematical Imaging and Vision
LS-MMRM '09 Proceedings of the First ACM workshop on Large-scale multimedia retrieval and mining
Sparse reconstruction by separable approximation
IEEE Transactions on Signal Processing
Nonlinear filtering for sparse signal recovery from incomplete measurements
IEEE Transactions on Signal Processing
Efficient minimization method for a generalized total variation functional
IEEE Transactions on Image Processing
A fast multilevel algorithm for wavelet-regularized image restoration
IEEE Transactions on Image Processing
Nonlinear regularization techniques for seismic tomography
Journal of Computational Physics
IEEE Transactions on Image Processing
Stagewise weak gradient pursuits
IEEE Transactions on Signal Processing
A SURE approach for digital signal/image deconvolution problems
IEEE Transactions on Signal Processing
A subband adaptive iterative shrinkage/thresholding algorithm
IEEE Transactions on Signal Processing
Image restoration by mixture modelling of an overcomplete linear representation
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
A priori guided reconstruction for FDOT using mixed norms
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
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Fast image recovery using variable splitting and constrained optimization
IEEE Transactions on Image Processing
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Restoration of Poissonian images using alternating direction optimization
IEEE Transactions on Image Processing
Image reconstruction by an alternating minimisation
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Effective image restorations using a novel spatial adaptive prior
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Restoration of images based on subspace optimization accelerating augmented Lagrangian approach
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Exact optimization for the l1-Compressive Sensing problem using a modified Dantzig-Wolfe method
Theoretical Computer Science
A non-adapted sparse approximation of PDEs with stochastic inputs
Journal of Computational Physics
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Sparse Signal Reconstruction via Iterative Support Detection
SIAM Journal on Imaging Sciences
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Illumination decomposition for material recoloring with consistent interreflections
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Super-Linear Convergence of Dual Augmented Lagrangian Algorithm for Sparsity Regularized Estimation
The Journal of Machine Learning Research
Deconvolving Poissonian images by a novel hybrid variational model
Journal of Visual Communication and Image Representation
An envelope signal based deconvolution algorithm for ultrasound imaging
Signal Processing
Analysis and Generalizations of the Linearized Bregman Method
SIAM Journal on Imaging Sciences
Large Scale Bayesian Inference and Experimental Design for Sparse Linear Models
SIAM Journal on Imaging Sciences
NESTA: A Fast and Accurate First-Order Method for Sparse Recovery
SIAM Journal on Imaging Sciences
Alternating Direction Method for Image Inpainting in Wavelet Domains
SIAM Journal on Imaging Sciences
Efficient minimization for dictionary based sparse representation and signal recovery
Proceedings of the 4th International Symposium on Applied Sciences in Biomedical and Communication Technologies
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Journal of Mathematical Imaging and Vision
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Computers & Geosciences
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Computers & Geosciences
Computational Optimization and Applications
A Simple Compressive Sensing Algorithm for Parallel Many-Core Architectures
Journal of Signal Processing Systems
A fast algorithm for nonconvex approaches to sparse recovery problems
Signal Processing
Robust spectral regression for face recognition
Neurocomputing
Information Sciences: an International Journal
Total variation regularization algorithms for images corrupted with different noise models: a review
Journal of Electrical and Computer Engineering
Engineering Applications of Artificial Intelligence
Journal of Mathematical Imaging and Vision
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Iterative shrinkage/thresholding (1ST) algorithms have been recently proposed to handle a class of convex unconstrained optimization problems arising in image restoration and other linear inverse problems. This class of problems results from combining a linear observation model with a nonquadratic regularizer (e.g., total variation or wavelet-based regularization). It happens that the convergence rate of these 1ST algorithms depends heavily on the linear observation operator, becoming very slow when this operator is ill-conditioned or ill-posed. In this paper, we introduce two-step 1ST (TwIST) algorithms, exhibiting much faster convergence rate than 1ST for ill-conditioned problems. For a vast class of nonquadratic convex regularizers (lscrP norms, some Besov norms, and total variation), we show that TwIST converges to a minimizer of the objective function, for a given range of values of its parameters. For noninvertible observation operators, we introduce a monotonic version of TwIST (MTwIST); although the convergence proof does not apply to this scenario, we give experimental evidence that MTwIST exhibits similar speed gains over IST. The effectiveness of the new methods are experimentally confirmed on problems of image deconvolution and of restoration with missing samples.