Compressed Remote Sensing of Sparse Objects

Albert Fannjiang, Thomas Strohmer, Pengchong Yan

Abstract: The linear inverse source and scattering problems are studied from the perspective of compressed sensing. By introducing the sensor as well as target ensembles, the maximum number of recoverable targets is proved to be at least proportional to the number of measurement data modulo a log-square factor with overwhelming probability. Important contributions include the discoveries of the threshold aperture, consistent with the classical Rayleigh criterion, and the incoherence effect induced by random antenna locations. The predictions of theorems are confirmed by numerical simulations.