Claire Boyer, “Sampling rates for l1-synthesis”
Claire Boyer, PhD
Assistant Professor
Sorbonne Université
Title: “Sampling rates for l1-synthesis”
Abstract: 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).
Biography: Claire Boyer was an associate member of the mathematics department of the ENS Ulm from 2017 to 2020, and is an assistant professor at Sorbonne Université since 2016. Her research areas are at the crossroads of compressed sensing, inverse problems, high-dimensional statistics, optimization, and machine learning with missing data.
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Meeting ID: 995 6750 4456