  The linear inverse source and scattering problems are studied from the
perspective of compressed sensing, in particular the idea that sufficient
incoherence and sparsity guarantee uniqueness of the solution. 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 of the analysis include the discoveries of the threshold
aperture, consistent with the classical Rayleigh criterion, and the decoherence
effect induced by random antenna locations. The prediction of theorems are
confirmed by numerical simulations.
