International Journal of Sensor Networks
Proximal Algorithms for Multicomponent Image Recovery Problems
Journal of Mathematical Imaging and Vision
An envelope signal based deconvolution algorithm for ultrasound imaging
Signal Processing
Foundations and Trends® in Machine Learning
Block-Based Compressed Sensing of Images and Video
Foundations and Trends in Signal Processing
An alternating direction method for finding Dantzig selectors
Computational Statistics & Data Analysis
Journal of Mathematical Imaging and Vision
Structured sparsity via alternating direction methods
The Journal of Machine Learning Research
Fast gradient vector flow computation based on augmented Lagrangian method
Pattern Recognition Letters
Joint sparsity-based robust multimodal biometrics recognition
ECCV'12 Proceedings of the 12th international conference on Computer Vision - Volume Part III
Sparse methods for biomedical data
ACM SIGKDD Explorations Newsletter
Fast restoration of nonuniform blurred images
IScIDE'12 Proceedings of the third Sino-foreign-interchange conference on Intelligent Science and Intelligent Data Engineering
An effective dual method for multiplicative noise removal
Journal of Visual Communication and Image Representation
A coupled variational model for image denoising using a duality strategy and split Bregman
Multidimensional Systems and Signal Processing
Journal of Mathematical Imaging and Vision
Hi-index | 0.01 |
We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly nonsmooth) regularizer is minimized under the constraint that the solution explains the observations sufficiently well. Although the regularizer and constraint are usually convex, several particular features of these problems (huge dimensionality, nonsmoothness) preclude the use of off-the-shelf optimization tools and have stimulated a considerable amount of research. In this paper, we propose a new efficient algorithm to handle one class of constrained problems (often known as basis pursuit denoising) tailored to image recovery applications. The proposed algorithm, which belongs to the family of augmented Lagrangian methods, can be used to deal with a variety of imaging IPLIP, including deconvolution and reconstruction from compressive observations (such as MRI), using either total-variation or wavelet-based (or, more generally, frame-based) regularization. The proposed algorithm is an instance of the so-called alternating direction method of multipliers, for which convergence sufficient conditions are known; we show that these conditions are satisfied by the proposed algorithm. Experiments on a set of image restoration and reconstruction benchmark problems show that the proposed algorithm is a strong contender for the state-of-the-art.