687 research outputs found
A greedy approach to sparse poisson denoising
International audienceIn this paper we propose a greedy method combined with the Moreau-Yosida regularization of the Poisson likelihood in order to restore images corrupted by Poisson noise. The regularization provides us with a data fidelity term with nice properties which we minimize under sparsity constraints. To do so, we use a greedy method based on a generalization of the well-known CoSaMP algorithm. We introduce a new convergence analysis of the algorithm which extends it use outside of the usual scope of convex functions. We provide numerical experiments which show the soundness of the method compared to the convex 1 -norm relaxation of the problem
Sparsity Based Poisson Denoising with Dictionary Learning
The problem of Poisson denoising appears in various imaging applications,
such as low-light photography, medical imaging and microscopy. In cases of high
SNR, several transformations exist so as to convert the Poisson noise into an
additive i.i.d. Gaussian noise, for which many effective algorithms are
available. However, in a low SNR regime, these transformations are
significantly less accurate, and a strategy that relies directly on the true
noise statistics is required. A recent work by Salmon et al. took this route,
proposing a patch-based exponential image representation model based on GMM
(Gaussian mixture model), leading to state-of-the-art results. In this paper,
we propose to harness sparse-representation modeling to the image patches,
adopting the same exponential idea. Our scheme uses a greedy pursuit with
boot-strapping based stopping condition and dictionary learning within the
denoising process. The reconstruction performance of the proposed scheme is
competitive with leading methods in high SNR, and achieving state-of-the-art
results in cases of low SNR.Comment: 13 pages, 9 figure
Generalized Subspace Pursuit and an application to sparse Poisson denoising
International audienceWe present a generalization of Subspace Pursuit, which seeks the k-sparse vector that minimizes a generic cost function. We introduce the Restricted Diagonal Property, which much like RIP in the classical setting, enables to control the convergence of Generalized Subspace Pursuit (GSP). To tackle the problem of Poisson denoising, we propose to use GSP together with the Moreau-Yosida approximation of the Poisson likelihood. Experiments were conducted on synthetic, exact sparse and natural images corrupted by Poisson noise. We study the influence of the different parameters and show that our approach performs better than Subspace Pursuit or l1-relaxed methods and compares favorably to state-of-art methods
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