Astronomical Image and Data Analysis (Astronomy and Astrophysics Library)
Astronomical Image and Data Analysis (Astronomy and Astrophysics Library)
Inpainting and Zooming Using Sparse Representations
The Computer Journal
A proximal iteration for deconvolving Poisson noisy images using sparse representations
IEEE Transactions on Image Processing
Nested Iterative Algorithms for Convex Constrained Image Recovery Problems
SIAM Journal on Imaging Sciences
Sparse Image and Signal Processing: Wavelets, Curvelets, Morphological Diversity
Sparse Image and Signal Processing: Wavelets, Curvelets, Morphological Diversity
Multiplicative noise removal using variable splitting and constrained optimization
IEEE Transactions on Image Processing
Restoration of Poissonian images using alternating direction optimization
IEEE Transactions on Image Processing
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In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by noise. A proper data fidelity term (log-likelihood) is introduced to reflect the statistics of the noise (e.g. Gaussian, Poisson) independently of the degradation. On the other hand, the regularization is constructed by assuming several a priori knowledge on the images. Piecing together the data fidelity and the prior terms, the solution to the inverse problem is cast as the minimization of a non-smooth convex functional. We establish the well-posedness of the optimization problem, characterize the corresponding minimizers for different kind of noises. Then we solve it by means of primal and primal-dual proximal splitting algorithms originating from the field of non-smooth convex optimization theory. Experimental results on deconvolution, inpainting and denoising with some comparison to prior methods are also reported.