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
Reconstruction of Wavelet Coefficients Using Total Variation Minimization
SIAM Journal on Scientific Computing
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Convex Optimization
Astronomical Image and Data Analysis (Astronomy and Astrophysics Library)
Astronomical Image and Data Analysis (Astronomy and Astrophysics Library)
A comparison of three total variation based texture extraction models
Journal of Visual Communication and Image Representation
Restoration of Chopped and Nodded Images by Framelets
SIAM Journal on Scientific Computing
Iterative Algorithms Based on Decoupling of Deblurring and Denoising for Image Restoration
SIAM Journal on Scientific Computing
Bregman-EM-TV Methods with Application to Optical Nanoscopy
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
A proximal iteration for deconvolving Poisson noisy images using sparse representations
IEEE Transactions on Image Processing
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
Linearized Bregman Iterations for Frame-Based Image Deblurring
SIAM Journal on Imaging Sciences
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
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
On the total variation dictionary model
IEEE Transactions on Image Processing
Fast image recovery using variable splitting and constrained optimization
IEEE Transactions on Image Processing
Restoration of Poissonian images using alternating direction optimization
IEEE Transactions on Image Processing
Restoration of images based on subspace optimization accelerating augmented Lagrangian approach
Journal of Computational and Applied Mathematics
Operator Splittings, Bregman Methods and Frame Shrinkage in Image Processing
International Journal of Computer Vision
Primal and Dual Bregman Methods with Application to Optical Nanoscopy
International Journal of Computer Vision
NESTA: A Fast and Accurate First-Order Method for Sparse Recovery
SIAM Journal on Imaging Sciences
Wavelet-based image estimation: an empirical Bayes approach using Jeffrey's noninformative prior
IEEE Transactions on Image Processing
Minimizing the total variation under a general convex constraint for image restoration
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration
IEEE Transactions on Image Processing
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In this paper, we propose a novel hybrid variational model for deconvolving Poissonian images by describing the original image as two parts - a cartoon part characterized by total variation, and a detailed part which has sparse representation over the wavelet basis. Fast and efficient iterative algorithms based on the split Bregman method are then employed. Under some conditions we prove the convergence properties of the iterative algorithms. Experiments demonstrate that the proposed hybrid model efficiently removes the noise and avoids the staircase effect simultaneously, which leads to a visually pleasant deconvolution result.