Quasi-linear Compressed Sensing and Applications in Asteroseismology

Massimo Fornasier*

Inspired by significant real-life applications, in particular, sparse phase retrieval and sparse pulsation frequency detection in Asteroseismology, we investigate a general framework for compressed sensing, where the measurements are quasi-linear. We formulate natural generalizations of the well-known Restricted Isometry Property (RIP) towards nonlinear measurements, which allow us to prove both unique identifiability of sparse signals as well as the convergence of recovery algorithms to compute them efficiently.

Mathematics Subject Classification: 94A20 47J25, 15B52

Keywords: quasi-linear compressed sensing, asteroseismology

Minisymposion: New Trends in Regularization Theory and Methods for Geomathematical Problems