Compressed sensing for inverse problems

by Dr Alessandro Felisi (University Genua)

Thursday Apr 10, 2025, 2:00 PM → 3:00 PM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

Compressed sensing allows for the recovery of sparse signals from a small number of measurements, which are proportional (up to logarithmic factors) to the sparsity of the unknown signal. Classical theory primarily considers randomly subsampled isometries in the finite-dimensional setting. In this talk, I will show how the theory of compressed sensing can also be rigorously applied to a variety of ill-posed inverse problems, including X-ray and photoacoustic tomography. Specifically, we will investigate, within a general framework, the relationship between the sparsity level of a signal, the ill-posedness of the problem, and the number of measurements required for stable reconstruction.