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
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
Spotlight-Mode Synthetic Aperture Radar: A Signal Processing Approach
Spotlight-Mode Synthetic Aperture Radar: A Signal Processing Approach
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Sparse reconstruction by separable approximation
IEEE Transactions on Signal Processing
Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
SIAM Journal on Imaging Sciences
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
A New Total Variation Method for Multiplicative Noise Removal
SIAM Journal on Imaging Sciences
The Split Bregman Method for L1-Regularized Problems
SIAM Journal on Imaging Sciences
A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
SIAM Journal on Imaging Sciences
Removing Multiplicative Noise by Douglas-Rachford Splitting Methods
Journal of Mathematical Imaging and Vision
Multiplicative Noise Removal Using L1 Fidelity on Frame Coefficients
Journal of Mathematical Imaging and Vision
Deblurring Poissonian images by split Bregman techniques
Journal of Visual Communication and Image Representation
Total variation restoration of speckled images using a split-Bregman algorithm
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration
IEEE Transactions on Image Processing
Restoration of Poissonian images using alternating direction optimization
IEEE Transactions on Image Processing
Journal of Mathematical Imaging and Vision
Linear inverse problems with various noise models and mixed regularizations
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
A new similarity measure for nonlocal filtering in the presence of multiplicative noise
Computational Statistics & Data Analysis
A convex relaxation method for computing exact global solutions for multiplicative noise removal
Journal of Computational and Applied Mathematics
Nonconvex sparse regularizer based speckle noise removal
Pattern Recognition
Fast reduction of speckle noise in real ultrasound images
Signal Processing
Journal of Computational and Applied Mathematics
Total variation regularization algorithms for images corrupted with different noise models: a review
Journal of Electrical and Computer Engineering
An effective dual method for multiplicative noise removal
Journal of Visual Communication and Image Representation
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Multiplicative noise (also known as speckle noise) models are central to the study of coherent imaging systems, such as synthetic aperture radar and sonar, and ultrasound and laser imaging. These models introduce two additional layers of difficulties with respect to the standard Gaussian additive noise scenario: 1) the noise is multiplied by (rather than added to) the original image; 2) the noise is not Gaussian, with Rayleigh and Gamma being commonly used densities. These two features of multiplicative noise models preclude the direct application of most state-of-the-art algorithms, which are designed for solving unconstrained optimization problems where the objective has two terms: a quadratic data term (log-likelihood), reflecting the additive and Gaussian nature of the noise, plus a convex (possibly nonsmooth) regularizer (e.g., a total variation or wavelet-based regularizer/prior). In this paper, we address these difficulties by: 1) converting the multiplicative model into an additive one by taking logarithms, as proposed by some other authors; 2) using variable splitting to obtain an equivalent constrained problem; and 3) dealing with this optimization problem using the augmented Lagrangian framework. A set of experiments shows that the proposed method, which we name MIDAL (multiplicative image denoising by augmented Lagrangian), yields state-of-the-art results both in terms of speed and denoising performance.