A coherence gradient method in waveform design for apertures

Abstract

Recently there has been much discussion of taking advantage of sparse approximation methods in detection. Methods such as compressive sensing use efficient basis decomposition methods such as Matching Pursuits in order to rapidly recover information sparsely sampled noisy data. Such methods rely on random or incoherent measurements of the target environment to recover data. In parallel, many compressive sensing techniques have been applied to estimation and detection problems in order to take advantage of not having complete information about a target environment to obtain a reliable estimation or detection result. Unfortunately, many real world target detection problems neither have random or incoherent measurements of the target environment, nor signal and noise characteristics that lend themselves to such assumptions of sparse approximation. We therefore propose a new set of constraints on the Matching Pursuits approach that enables rapid convergence of the sparse approximation method using a coherence constraint and gradient based search algorithm that enables a robust detection method with standard generalized likelihood detection methods.