Skip to Main content Skip to Navigation
Theses

Méthodes de programmation en nombres mixtes pour l'optimisation parcimonieuse en traitement du signal

Abstract : Sparse approximation aims to fit a linear model in a least-squares sense, with a small number of non-zero components (the L0 “norm”). Due to its combinatorial nature, it is often addressed by suboptimal methods. It was recently shown, however, that exact resolution could be performed through a mixed integer program(MIP) reformulation solved by a generic solver, implementing branch-and-bound techniques. This thesis addresses the L0-norm sparse approximation problem with tailored branch-andbound resolution methods, exploiting the mathematical structures of the problem. First, we show that each node evaluation amounts to solving an L1-norm problem, for which we propose dedicated methods. Then, we build an efficient exploration strategy exploiting the sparsity of the solution, by activating first the non-zero variables in the tree search. The proposed method outperforms the CPLEX solver, reducing the computation time and making it possible to address larger problems. In a second part of the thesis, we propose and study the MIP reformulations of the spectral unmixing problem with L0-norm sparsity more advanced structured sparsity constraints, which are usually addressed through relaxations in the literature. We show that, for problems with limited complexity (highly sparse solutions, good signal-to-noise ratio), such constraints can be accounted for exactly and improve the estimation quality over standard approaches.
Document type :
Theses
Complete list of metadata

https://tel.archives-ouvertes.fr/tel-03237601
Contributor : Abes Star :  Contact
Submitted on : Wednesday, May 26, 2021 - 4:55:11 PM
Last modification on : Tuesday, September 21, 2021 - 4:06:15 PM
Long-term archiving on: : Friday, August 27, 2021 - 8:36:25 PM

File

R_BENMHENNI_VG.pdf
Version validated by the jury (STAR)

Identifiers

  • HAL Id : tel-03237601, version 1

Citation

Ramzi Ben Mhenni. Méthodes de programmation en nombres mixtes pour l'optimisation parcimonieuse en traitement du signal. Traitement du signal et de l'image [eess.SP]. École centrale de Nantes, 2020. Français. ⟨NNT : 2020ECDN0008⟩. ⟨tel-03237601⟩

Share

Metrics

Record views

93

Files downloads

100