Sampling rates for l1-synthesis ou « Combien de projections sous-gaussiennes doit-on faire pour reconstruire un objet parcimonieux dans un dictionnaire redondant ? »
25/01/2021, 11:00, en ligne via Teams
This work investigates the problem of signal recovery from undersampled noisy sub-Gaussian measurements under the assumption of a synthesis-based sparsity model. Solving the l1-synthesis basis pursuit allows to simultaneously estimate a coefficient representation as well as the sought-for signal. However, due to linear dependencies within redundant dictionary atoms it might be impossible to identify a specific representation vector, although the actual signal is still successfully recovered. We study both estimation problems from a non-uniform, signal-dependent perspective. By utilizing results from linear inverse problems and convex geometry, we identify the sampling rate describing the phase transition of both formulations, and propose a « tight » estimated upper-bound.
This is a joint work with Maximilian März (TU Berlin), Jonas Kahn and Pierre Weiss (CNRS, Toulouse).