Fred K. Gruber

Time-reversal imaging with multiple signal classification considering multiple scattering between the targets

The time-reversal imaging with multiple signal classification method for the location of point targets developed within the framework of the Born approximation in Lehman and Devaney [“Transmission mode time-reversal super-resolution imaging,” J. Acoust. Soc. Am. 113, 2742–2753 (2003)] is generalized to incorporate multiple scattering between the targets. It is shown how the same method can be used in the location of point targets even if there is multiple scattering between them. On the other hand, both the conventional images and the calculated values of the target scattering amplitudes are scattering model-dependent.

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 (2004)] 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 (MUSIC) 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.

Time-Reversal MUSIC Imaging of Extended Targets

This paper develops, within a general framework that is applicable to rather arbitrary electromagnetic and acoustic remote sensing systems, a theory of time-reversal ldquomultiple signal classificationrdquo (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.

Subspace-based localization and inverse scattering of multiply scattering point targets

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.

Inverse source problem with reactive power constraint

This paper reports a general Lagrangian formulation for constrained electromagnetic inverse source problems. The formulation is applicable to different forms of inverse source problems having different constraints. Two possibilities are emphasized in the paper. One yields the usual minimum energy solution. The other establishes a new minimum energy solution with the additional constraint that the source has a prescribed reactive power (which can be zero). The latter solution incorporates the important reactive energy issues of an antenna which had not been considered before in the context of the inverse source problem. The new solution is shown to obey a homogeneous wave equation in the interior of the source volume, and expressions for the associated interior field and interaction power are also derived. The derived theory is illustrated for a canonical dipolar source and an alternative approach where the reactive power is minimized for a prescribed maximum functional energy is also presented. Advantage is taken of some of the results to briefly discuss some questions about fundamental antenna limits.

New Aspects of Electromagnetic Information Theory for Wireless and Antenna Systems

This paper investigates information-theoretic characterization, via Shannons information capacity and number of degrees of freedom, of wave radiation (antenna) and wireless propagation systems. Specifically, the paper derives, from the fundamental physical point of view of Maxwells equations describing electromagnetic fields, the Shannon information capacity of space-time wireless channels formed by electromagnetic sources and receivers in a known background medium. The theory is developed first for the case of sources working at a fixed frequency (time-harmonic case) and is expanded later to the more general case of temporally bandlimited systems (time-domain fields). In the bandlimited case we consider separately the two cases of time-limited and essentially bandlimited systems and of purely bandlimited systems. The developments take into account the physical radiated power constraint in addition to a constraint in the source L 2 norm which acts to avoid antenna superdirectivity. Based on such radiated power and current L 2 norm constraints we derive the Shannon information capacity of canonical wireless and antenna systems in free space, for a given additive Gaussian noise level, as well as an associated number of degrees of freedom resulting from such capacity calculations. The derived results also illustrate, from a new information-theoretic point of view, the transition from near to far fields.

Optical-Theorem-Based Coherent Scatterer Detection in Complex Environments

A new approach is proposed to detect scatterers embedded in reciprocal media from scattering data. The new method is rooted on physical considerations, in particular, on the optical theorem applicable to wavefields (e.g., acoustic, electromagnetic, and optical). The approach exploits insight gained from the optical theorem which assigns physical energy interpretations to the wave data from time reversal mirrors and cavities from which one can deduce the presence of unknown scatterers in unknown background media. The proposed approach is ideally suited for target detection in complex, highly reverberating unknown environments such as indoor facilities, caves, tunnels, and urban canyon.

Reinterpretation and Enhancement of Signal-Subspace-Based Imaging Methods for Extended Scatterers

Interior sampling and exterior sampling (or enclosure) signal-subspace-based imaging methodologies for extended scatterers derived in previous work are reformulated and reinterpreted in terms of the concepts of angles and distances between subspaces. The insight gained from this reformulation renders a broader, more encompassing inversion methodology based on a (pseudo) cross-coherence matrix associated to the singular vectors of the scattering or response matrix and the singular vectors intrinsic to a given, hypothesized support region for the scatterers (under a known background Greens function associated to a known embedding medium where the scatterers reside). A number of new imaging functionals based on that cross-coherence matrix are proposed and numerically shown to perform well in both imaging and shape reconstruction problems. The proposed approaches do not require for their implementation the estimation of a cutoff in the singular value spectrum separating signal from noise subspaces, which is a common computational difficulty in signal subspace methods. In the shape reconstruction context it is also shown how to combine the signal subspace approach with the level set method.

Generalized time-reversal imaging considering multiple scattering effects

This paper considers time-reversal (TR) imaging with the multiple signal classification (MUSIC) method for the location of point targets, not only in the usual framework of the Born approximation but also in more general nonlinear scattering frameworks where there is multiple scattering between the targets. This finding is important toward practical implementations of the TR technique facing multiple scattering effects. The super-resolution results of a previous paper (C. Prada et al., Acoust. Soc. Am., vol.114, p.235-243, 2003) can now be better characterized theoretically in the multiple scattering regime. We showed how both the conventional, backpropagated images of the principal eigenvectors and the predicted values of the target scattering amplitudes are scattering model-dependent.

Imaging of scatterers using canonical correlations

There is much interest in the application of subspace-based signal processing techniques for wavefield imaging of scatterers from the scattering matrix [1], [2], [3], [4], [5], [6], [7]. These approaches are part of the modern focus on so-called “qualitative” methods in inverse scattering [8]. Most of these methods are valid in the exact scattering regime including multiple scattering in which the inverse scattering problem is nonlinear.