We study a variational formulation for reconstructing nonlinearly distorted signals corrupted with a Poisson-Gaussian noise. In this situation, the data fidelity term consists of a sum of a weighted least squares term and a logarithmic one. Both of them are precomposed by a nonlinearity, modelling a clipping effect, which is assumed to be rational. A regularization term, being a piecewise rational approximation of the ℓ0 function provides a suitable sparsity measure with respect to a preset linear operator. We propose a global optimization approach for such a problem. More specifically, it is first transformed into a generalized moment problem by introducing some auxiliary variables. Then, a hierarchy of semidefinite programming relaxations is built. Numerical examples show the good performance of the proposed approach.
Authors
- Arthur Marmin,
- dr inż. Anna Węsierska link open in new tab ,
- dr Marc Castella,
- Jean-Christophe Pesquet
Additional information
- DOI
- Digital Object Identifier link open in new tab 10.1109/lsp.2020.2998699
- Category
- Publikacja w czasopiśmie
- Type
- artykuły w czasopismach
- Language
- angielski
- Publication year
- 2020
