
Research Article
Linear inverse problems with various noise models and mixed regularizations
@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
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.