Adaptive compressed sensing for sparse signals in noise

This paper studies the problem of recovering a signal with a sparse representation in a given orthonormal basis using as few noisy observations as possible. Herein, observations are subject to the type of background clutter noise encountered in radar applications. Given this model, this paper proves for the first time that highly sparse signals contaminated with Gaussian background noise can be recovered by adaptive methods using fewer noisy linear measurements than required by any possible recovery method based on non-adaptive Gaussian measurement ensembles.