Imaging in random media by two-point coherent interferometry

TL;DR

This paper introduces a novel two-point coherent interferometric imaging method that achieves high-resolution, statistically stable images through random media by leveraging cross correlations and advanced signal processing techniques.

Contribution

It presents new methods for high-resolution imaging in random media using two-point CINT, including phase retrieval, eigenvector analysis, and optimization, improving upon standard CINT approaches.

Findings

Two-point CINT provides stable, high-resolution images.

The proposed methods outperform standard CINT in simulations.

The techniques are applicable to synthetic aperture radar data.

Abstract

This paper considers wave-based imaging through a heterogeneous (random) scattering medium. The goal is to estimate the support of the reflectivity function of a remote scene from measurements of the backscattered wave field. The proposed imaging methodology is based on the coherent interferometric (CINT) approach that exploits the local empirical cross correlations of the measurements of the wave field. The standard CINT images are known to be robust (statistically stable) with respect to the random medium, but the stability comes at the expense of a loss of resolution. This paper shows that a two-point CINT function contains the information needed to obtain statistically stable and high-resolution images. Different methods to build such images are presented, theoretically analyzed and compared with the standard imaging approaches using numerical simulations. The first method involves a phase-retrieval step to extract the reflectivity function from the modulus of its Fourier transform. The second method involves the evaluation of the leading eigenvector of the two-point CINT imaging function seen as the kernel of a linear operator. The third method uses an optimization step to extract the reflectivity function from some cross products of its Fourier transform. The presentation is for the synthetic aperture radar data acquisition setup, where a moving sensor probes the scene with signals emitted periodically and records the resulting backscattered wave. The generalization to other imaging setups, with passive or active arrays of sensors, is discussed briefly.