Communications in Information and Systems

Volume 5 (2005)

Number 2

Maximum likelihood estimation of point scatterers for computational time-reversal imaging

Pages: 227 – 256

DOI: http://dx.doi.org/10.4310/CIS.2005.v5.n2.a4

Authors

Arye Nehorai (ECE Department, The University of Illinois at Chicago, Chicago, Il., U.S.A.)

Gang Shi (ECE Department, The University of Illinois at Chicago, Chicago, Il., U.S.A.)

Abstract

We present a statistical framework for the fixed-frequency computational timereversal 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.

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