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1st International ICST Workshop on New Computational Methods for Inverse Problems

Research Article

Linear inverse problems with various noise models and mixed regularizations

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  • @INPROCEEDINGS{10.4108/icst.valuetools.2011.246491,
        author={Fran\`{e}ois-Xavier Dup\^{e} and Jalal Fadili and Jean-Luc Starck},
        title={Linear inverse problems with various noise models and mixed regularizations},
        proceedings={1st International ICST Workshop on New Computational Methods for Inverse Problems},
        publisher={ACM},
        proceedings_a={NCMIP},
        year={2012},
        month={6},
        keywords={inverse problems poisson noise gaussian noise multiplicative noise duality proximity operator sparsity},
        doi={10.4108/icst.valuetools.2011.246491}
    }
    
  • François-Xavier Dupé
    Jalal Fadili
    Jean-Luc Starck
    Year: 2012
    Linear inverse problems with various noise models and mixed regularizations
    NCMIP
    ICST
    DOI: 10.4108/icst.valuetools.2011.246491
François-Xavier Dupé1,*, Jalal Fadili2, Jean-Luc Starck1
  • 1: CEA
  • 2: GREYC
*Contact email: francois-xavier.dupe@cea.fr

Abstract

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.

Keywords
inverse problems poisson noise gaussian noise multiplicative noise duality proximity operator sparsity
Published
2012-06-26
Publisher
ACM
http://dx.doi.org/10.4108/icst.valuetools.2011.246491
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