Maximum Likelihood Estimation of Point Scatterers for Computational Time-reversal Imaging

Abstract

We present a statistical framework for the fixed-frequency computational time-reversal imaging problem assuming point scatterers in a known background medium. Our statistical measurement models are based on the physical models of the multistatic response matrix, the distorted wave Born approximation and Foldy-Lax multiple scattering models. We develop maximum likelihood (ML) estimators of the locations and reflection parameters of the scatterers. Using a simplified single-scatterer model, we also propose a likelihood time-reversal imaging technique which is suboptimal but computationally efficient and can be used to initialize the ML estimation. We generalize the fixed-frequency likelihood imaging to multiple frequencies, and demonstrate its effectiveness in resolving the grating lobes of a sparse array. This enables to achieve high resolution by deploying a large-aperture array consisting of a small number of antennas while avoiding spatial ambiguity. Numerical and experimental examples are used to illustrate the applicability of our results.