Mathematical Programming: Series A and B
Multiresolution support applied to image filtering and restoration
Graphical Models and Image Processing
Generalized cross validation for wavelet thresholding
Signal Processing
Deconvolution of images and spectra (2nd ed.)
Deconvolution of images and spectra (2nd ed.)
A Modified Forward-Backward Splitting Method for Maximal Monotone Mappings
SIAM Journal on Control and Optimization
Digital Image Restoration
Wavelets and curvelets for image deconvolution: a combined approach
Signal Processing - Special section: Security of data hiding technologies
DeQuant: a flexible multiresolution restoration framework
Signal Processing
DeQuant: a flexible multiresolution restoration framework
Signal Processing
Adaptive Wavelet Galerkin Methods for Linear Inverse Problems
SIAM Journal on Numerical Analysis
Astronomical Image and Data Analysis (Astronomy and Astrophysics Library)
Astronomical Image and Data Analysis (Astronomy and Astrophysics Library)
Proximal Thresholding Algorithm for Minimization over Orthonormal Bases
SIAM Journal on Optimization
Inpainting and Zooming Using Sparse Representations
The Computer Journal
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A statistical multiscale framework for Poisson inverse problems
IEEE Transactions on Information Theory
Poisson intensity estimation for tomographic data using a wavelet shrinkage approach
IEEE Transactions on Information Theory
An EM algorithm for wavelet-based image restoration
IEEE Transactions on Image Processing
Deconvolution of poissonian images via iterative shrinkage
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
Compressed sensing performance bounds under Poisson noise
IEEE Transactions on Signal Processing
Restoration of Poissonian images using alternating direction optimization
IEEE Transactions on Image Processing
Deconvolving Poissonian images by a novel hybrid variational model
Journal of Visual Communication and Image Representation
Regularizing parameter estimation for Poisson noisy image restoration
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
Linear inverse problems with various noise models and mixed regularizations
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
A Novel Sparsity Reconstruction Method from Poisson Data for 3D Bioluminescence Tomography
Journal of Scientific Computing
Adaptive noise reduction of scintigrams with a wavelet transform
Journal of Biomedical Imaging
A Simple Compressive Sensing Algorithm for Parallel Many-Core Architectures
Journal of Signal Processing Systems
Total variation regularization algorithms for images corrupted with different noise models: a review
Journal of Electrical and Computer Engineering
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We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transforms. Our key contributions are as follows. First, we handle the Poisson noise properly by using the Anscombe variance stabilizing transform leading to a nonlinear degradation equation with additive Gaussian noise. Second, the deconvolution problem is formulated as the minimization of a convex functional with a data-fidelity term reflecting the noise properties, and a nonsmooth sparsity-promoting penalty over the image representation coefficients (e.g., l1-norm). An additional term is also included in the functional to ensure positivity of the restored image. Third, a fast iterative forward-backward splitting algorithm is proposed to solve the minimization problem. We derive existence and uniqueness conditions of the solution, and establish convergence of the iterative algorithm. Finally, a GCV-based model selection procedure is proposed to objectively select the regularization parameter. Experimental results are carried out to show the striking benefits gained from taking into account the Poisson statistics of the noise. These results also suggest that using sparse-domain regularization may be tractable in many deconvolution applications with Poisson noise such as astronomy and microscopy.