Edwin A. Marengo

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.

The inverse source problem of electromagnetics: linear inversion formulation and minimum energy solution

We address the inverse source problem of finding the time-harmonic current distribution (source) with minimum L/sup 2/ norm (minimum energy) that generates a prescribed electromagnetic field outside the sources 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/sup 2/ norm-current distribution consistent with the data.

Nonradiating and minimum energy sources and their fields: generalized source inversion theory and applications

A new general framework for characterizing scalar and electromagnetic (EM) nonradiating (NR) and minimum energy (ME) sources and their fields is developed that is of interest for both radiation and source reconstruction problems. NR sources are characterized in connection with the concept of reciprocity as nonreceptors. Localized ME sources are shown to be free fields truncated within the sources support. A new source analysis tool is developed that is based on the decomposition of a source and its field into their radiating and NR components. The individual radiating and reactive energy roles of the radiating and NR parts of a source are characterized. The general theory is illustrated with a time-harmonic EM example.

Illustration of the role of multiple scattering in subwavelength imaging from far-field measurements

Recently it has been proposed that the classical diffraction limit could be overcome by taking into account multiple scattering effects to describe the interaction of a probing wave and the object to be imaged [Phys. Rev. E73, 036619 (2006)]. Here this idea is illustrated by considering two point scatterers spaced much less than a wavelength apart. It is observed that while under the Born approximation the scattered field pattern is similar to that of a monopole source centered between the scatterers, multiple scattering leads to a more complicated pattern. This additional complexity carries information about the subwavelength structure and can lead to superresolution in the presence of large noise levels. Moreover, it is pointed out that the additional information due to multiple scattering is interpreted as a form of coherent noise by inversion algorithms based on the Born approximation.

Inverse source problem and minimum-energy sources

We present a new linear inversion formalism for the scalar inverse source problem in three-dimensional and one-dimensional (1D) spaces, from which a number of previously unknown results on minimum-energy (ME) sources and their fields readily follow. ME sources, of specified support, are shown to obey a homogeneous Helmholtz equation in the interior of that support. As a consequence of that result, the fields produced by ME sources are shown to obey an iterated homogeneous Helmholtz equation. By solving the latter equation, we arrive at a new Green-function representation of the field produced by a ME source. It is also shown that any square-integrable (L2), compactly supported source that possesses a continuous normal derivative on the boundary of its support must possess a nonradiating (NR) component. A procedure based on our results on the inverse source problem and ME sources is described to uniquely decompose an L2 source of specified support and its field into the sum of a radiating and a NR part. The general theory that is developed is illustrated for the special cases of a homogeneous source in 1D space and a spherically symmetric source.

Inverse Source Problem in Nonhomogeneous Background Media

The scalar wave inverse source problem (ISP) of determining an unknown radiating source from knowledge of the field it generates outside its region of localization is investigated for the case in which the source is embedded in a nonhomogeneous medium with known index of refraction profile

Inverse source problem with reactive power constraint

n(\mathbf{r})