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
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Smooth minimization of non-smooth functions
Mathematical Programming: Series A and B
Some First-Order Algorithms for Total Variation Based Image Restoration
Journal of Mathematical Imaging and Vision
Efficient Schemes for Total Variation Minimization Under Constraints in Image Processing
SIAM Journal on Scientific Computing
The Split Bregman Method for L1-Regularized Problems
SIAM Journal on Imaging Sciences
Nested Iterative Algorithms for Convex Constrained Image Recovery Problems
SIAM Journal on Imaging Sciences
A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
SIAM Journal on Imaging Sciences
IEEE Transactions on Image Processing
Total variation minimization and a class of binary MRF models
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Penalized maximum-likelihood image reconstruction using space-alternating generalized EM algorithms
IEEE Transactions on Image Processing
Multiplicative noise removal using variable splitting and constrained optimization
IEEE Transactions on Image Processing
Practical methods for convex multi-view reconstruction
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part IV
Restoration of Poissonian images using alternating direction optimization
IEEE Transactions on Image Processing
SIAM Journal on Scientific Computing
Operator Splittings, Bregman Methods and Frame Shrinkage in Image Processing
International Journal of Computer Vision
Deconvolving Poissonian images by a novel hybrid variational model
Journal of Visual Communication and Image Representation
A Spatial Regularization Approach for Vector Quantization
Journal of Mathematical Imaging and Vision
Inexact Alternating Direction Methods for Image Recovery
SIAM Journal on Scientific Computing
A Novel Sparsity Reconstruction Method from Poisson Data for 3D Bioluminescence Tomography
Journal of Scientific Computing
Total variation blind deconvolution employing split Bregman iteration
Journal of Visual Communication and Image Representation
Dual Norm Based Iterative Methods for Image Restoration
Journal of Mathematical Imaging and Vision
Structured sparsity via alternating direction methods
The Journal of Machine Learning Research
A relaxed split bregman iteration for total variation regularized image denoising
ICIC'12 Proceedings of the 8th international conference on Intelligent Computing Theories and Applications
A convex relaxation method for computing exact global solutions for multiplicative noise removal
Journal of Computational and Applied Mathematics
Coupling Image Restoration and Segmentation: A Generalized Linear Model/Bregman Perspective
International Journal of Computer Vision
A proximal parallel splitting method for minimizing sum of convex functions with linear constraints
Journal of Computational and Applied Mathematics
Computers in Biology and Medicine
Image Restoration via Tight Frame Regularization and Local Constraints
Journal of Scientific Computing
An effective dual method for multiplicative noise removal
Journal of Visual Communication and Image Representation
A New Poisson Noise Filter Based on Weights Optimization
Journal of Scientific Computing
Homogeneous Penalizers and Constraints in Convex Image Restoration
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
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The restoration of blurred images corrupted by Poisson noise is an important task in various applications such as astronomical imaging, electronic microscopy, single particle emission computed tomography (SPECT) and positron emission tomography (PET). In this paper, we focus on solving this task by minimizing an energy functional consisting of the I-divergence as similarity term and the TV regularization term. Our minimizing algorithm uses alternating split Bregman techniques (alternating direction method of multipliers) which can be reinterpreted as Douglas-Rachford splitting applied to the dual problem. In contrast to recently developed iterative algorithms, our algorithm contains no inner iterations and produces nonnegative images. The high efficiency of our algorithm in comparison to other recently developed algorithms to minimize the same functional is demonstrated by artificial and real-world numerical examples.