Adaptive Group Testing Strategies for Target Detection and Localization in Noisy Environments

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. As opposed to previous studies, this paper models observations which are subject to the type of ‘clutter noise’ encountered in radar applications (i.e., the measurements used influence the observed noise). Given this model, the paper develops bounds on the number of measurements required to reconstruct the support of the signal and the signal itself up to any given accuracy level when the measurement noise is Gaussian using non-adaptive and adaptive measurement strategies. Further, the paper demonstrates that group testing measurement constructions may be combined with statistical binary detection and estimation methods to produce practical and computationally efficient adaptive algorithms for sparse signal approximation and support recovery. In particular, the paper proves that a wide class of sparse signals can be recovered by adaptive methods using fewer noisy linear measurements than required by any recovery method based on non-adaptive Gaussian measurement ensembles. This result demonstrates an improvement over previous non-adaptive methods in the compressed sensing literature for sparse support pattern recovery in the sublinear-sparse support regime under the measurement model considered herein.