Gwen SAMAIN : PhD defense – Branch-and-bound algorithm for efficient resolution of sparse optimization problems.

Abstract: Numerous inverse problems in signal processing, statistics, biomedical imaging, astronomy and machine learning can be cast as the search for the best pattern combination fitting measurements, these patterns being taken from a known dictionary. The sparsity of the problem comes from the small number of patterns desired, using a l0 term. Several standard methods, among which greedy algorithms (OMP, OLS) and convex reformulations (most notably the l1-norm reformulation), provide approximate solutions to this l0 problem. More recently, methods able to solve exactly the l0 problem were designed, using branch-and-bound algorithms. This PhD thesis has two goals. First, explore possible accelerations of current branch-and-bound algorithms dedicated to the l0 problem. Then, extend these branch-and-bound algorithms to the case of structured sparsity, where we are not looking for a small number of patterns fitting data, but a small number of groups of patterns fitting data. These contributions lead to the development of an open-source code publicly released.

https://ec-nantes.zoom.us/j/2977696674
Meeting ID: 297 769 6674
Passcode: &58Vv@KP