A statistical approach to target detection and localization in the presence of noise

The problem addressed in this paper is the combined detection and localization of a point reflector embedded in a medium by sensor array imaging when the array response matrix is obtained in a noisy environment. We consider additive measurement noise or a clutter noise in the multiple scattering regime. We study a detection test based on reverse-time migration of the array response matrix that is the most powerful for a given false alarm rate and compare it with a test based on the singular values of the response matrix. Moreover, we show that reflector localization should be performed with reverse-time migration rather than any other form of weighted-subspace migration and we give the standard deviation of the localization error.