Claire Boyer, PhD
Sampling rates for l1-synthesis
Abstract : Thiswork investigates the problem of signal recoveryfrom undersampled noisysub-Gaussian measurements under the assumption of asynthesis-based sparsitymodel. Solving the l1-synthesis basis pursuit allows to simultaneously estimatea coefficient representation as well as the sought-for signal. However, due tolinear dependencies within redundant dictionary atoms it might be impossible toidentify a specific representation vector, although the actual signal is stillsuccessfully recovered. We study both estimation problems from a non-uniform,signal-dependent perspective. By utilizing results from linear inverse problemsand convex geometry, we identify the sampling rate describing the phasetransition of both formulations, and propose a “tight” estimatedupper-bound.
Thisis a joint work with Maximilian März (TU Berlin), Jonas Kahn and Pierre Weiss(CNRS, Toulouse).
Bio: ClaireBoyer was an associate member of the mathematics department of the ENS Ulm from2017 to 2020 and is an assistant professorat Sorbonne Université since2016.
Herresearch areas are at the crossroads of compressed sensing, inverse problems,high-dimensional statistics, optimization, and machine learningwith missing data.