Sampling Rates for ℓ1-Synthesis

Claire Boyer
LPSM, Sorbonne University

Date(s) : 06/11/2020   iCal
14 h 30 min - 15 h 30 min

Sampling Rates for ℓ1-Synthesis ou « Combien de projections sous-gaussiennes doit-on faire pour reconstruire un objet parcimonieux dans un dictionnaire redondant ? »

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).

Slides :

Site Nord, CMI, Salle de Séminaire R164 (1er étage)


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