Deblurring Poissonian images by split Bregman techniques
Journal of Visual Communication and Image Representation
Compressed sensing performance bounds under Poisson noise
IEEE Transactions on Signal Processing
Deconvolving Poissonian images by a novel hybrid variational model
Journal of Visual Communication and Image Representation
Linear inverse problems with various noise models and mixed regularizations
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
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The objective of this paper is to develop methods for solving image recovery problems subject to constraints on the solution. More precisely, we will be interested in problems which can be formulated as the minimization over a closed convex constraint set of the sum of two convex functions $f$ and $g$, where $f$ may be nonsmooth and $g$ is differentiable with a Lipschitz-continuous gradient. To reach this goal, we derive two types of algorithms that combine forward-backward and Douglas-Rachford iterations. The weak convergence of the proposed algorithms is proved. In the case when the Lipschitz-continuity property of the gradient of $g$ is not satisfied, we also show that, under some assumptions, it remains possible to apply these methods to the considered optimization problem by making use of a quadratic extension technique. The effectiveness of the algorithms is demonstrated for two wavelet-based image restoration problems involving a signal-dependent Gaussian noise and a Poisson noise, respectively.