Time-reversal-based imaging and inverse scattering of multiply scattering point targets

The treatment of time-reversal imaging of multiply scattering point targets developed by the present authors in Gruber et al. ͓"Time-reversal imaging with multiple signal classification considering multiple scattering between the targets," J. Acoust. Soc. Am., 115, 3042-3047 ͑2004͔͒ is reformulated and extended to the estimation of the target scattering strengths using the Foldy-Lax multiple scattering model. It is shown that the time-reversal multiple signal classification ͑MUSIC͒ pseudospectrum computed using the background Green function as the steering vector yields accurate estimates of the target locations, even in the presence of strong multiple scattering between the targets, and that the target scattering strengths are readily computed from the so-determined target locations using a nonlinear iterative algorithm. The paper includes computer simulations illustrating the theory and algorithms presented in the paper.

This paper develops, within a general framework that is applicable to rather arbitrary electromagnetic and acoustic remote sensing systems, a theory of time-reversal "MUltiple Signal Classification" (MUSIC)-based imaging of extended (nonpoint-like) scatterers (targets). The general analysis applies to arbitrary remote sensing geometry and sheds light onto how the singular system of the scattering matrix relates to the geometrical and propagation characteristics of the entire transmitter-target-receiver system and how to use this effect for imaging. All the developments are derived within exact scattering theory which includes multiple scattering effects. The derived time-reversal MUSIC methods include both interior sampling, as well as exterior sampling (or enclosure) approaches. For presentation simplicity, particular attention is given to the time-harmonic case where the informational wave modes employed for target interrogation are purely spatial, but the corresponding generalization to broadband fields is also given. This paper includes computer simulations illustrating the derived theory and algorithms.

We address the inverse source problem of finding the time-harmonic current distribution (source) with minimum L 2 norm (minimum energy) that generates a prescribed electromagnetic field outside the source's region of support. Using the well-known multipole expansion of the electromagnetic field we compute (via a linear operator formalism) the sought-after minimum L 2 norm-current distribution consistent with the data. Index Terms-Electromagnetic scattering, inverse source problem. I. INTRODUCTION The inverse source problem consists of reconstructing a radiating source distribution from knowledge of the field it generates outside its

The nonlinear inverse scattering problem of estimating the locations and scattering strengths or reflectivities of a number of small, point-like inhomogeneities (targets) to a known background medium from single-snapshot active wave sensor array data is investigated in connection with time-reversal multiple signal classification and an alternative signal subspace method which is based on search in high-dimensional parameter space and which is found to outperform the time-reversal approach in number of localizable targets and in estimation variance. A noniterative formula for the calculation of the target reflectivities is derived which completes the solution of the nonlinear inverse scattering problem for the general case when there is significant multiple scattering between the targets. The paper includes computer simulations illustrating the theory and methods discussed in the paper.