An approximate solution for the compressed sensing problem using statistical mechanics tool

par Dr Anna Paola Muntoni (DISAT, Polytechnic University of Turin, Italy.)

mardi 2 mai 2023, 14:00 → 15:00 Europe/Paris

Abstract:

Many interesting problems in fields ranging from telecommunications to computational biology can be formalized in terms of large underdetermined systems of linear equations with additional constraints or regularizers. One of the most studied, the compressed sensing (CS) problem, consists in finding the solution with the smallest number of non-zero components of a given system of linear equations.

In this talk, I will address the CS problem within a Bayesian inference framework where the sparsity constraint is remapped into a singular prior distribution (called Spike-and-Slab or Bernoulli–Gauss). A solution to the problem is attempted through the computation of marginal distributions via Expectation Propagation, an iterative computational scheme originally developed in statistical physics.

Keywords:
compressed sensing, expectation propagation, Bayesian inference