Noniterative analytical formula for inverse scattering of multiply scattering point targets

TR-MUSIC inversion of the density and compressibility contrasts of point scatterers

Time-reversal imaging with multiple signal classification (TR-MUSIC) is a super-resolution ultrasound imaging method for detecting point scatterers. This algorithm assumes that there is no contrast between the density of the point targets and that of the background medium, and that ultrasound scattering is caused only by the compressibility contrast. We modify the TR-MUSIC algorithm to account for ultrasound scattering from point targets with both density and compressibility contrasts. In addition, we develop an inversion method for estimating the density and compressibility contrasts of point scatterers with known locations. This approach is an extension of the inversion method previously developed by Devaney et al. for estimating the scattering strengths of point targets that have no density contrasts relative to the background medium. We use numerical phantom data to demonstrate that our new TR-MUSIC inversion algorithm can reliably estimate the density and compressibility contrasts of point scatterers. The estimates of these properties could be used for distinguishing breast calcifications from other tissue scatterers.

Multiple signal classification method for detecting point-like scatterers embedded in an inhomogeneous background medium

The multiple signal classification (MUSIC) type method has been widely used to detect point-like scatterers embedded in a homogeneous background medium. This paper extends the MUSIC-type method to the detection of point-like scatterers that are embedded in an inhomogeneous background. Although the background Green's function at each test point is not directly available in inhomogeneous background scenario, this paper proposes an approach, based on the finite element method, to simultaneously obtain the Green's function at all test points. Numerical simulations illustrate the efficacy of the proposed theory and algorithm presented in this paper, and some interesting observations, which are absent in homogeneous background scenario, are highlighted and discussed.

Application of signal-subspace and optimization methods in reconstructing extended scatterers

A signal-subspace approach to reconstruct the permittivities of extended scatterers in two-dimensional settings is proposed. A portion of the scatterers' information is retrieved by the signal-subspace method, and the remaining part is obtained by solving a nonlinear least-squares problem. The method exhibits several strengths, including robustness against noise, fast convergence, less scattering data, high resolution, and the ability to deal with scatterers of special shapes.

Signal-subspace method approach to the intensity-only electromagnetic inverse scattering problem

This paper investigates the signal-subspace method approach to solve the electromagnetic inverse scattering problem using intensity-only (phase-free) data. Due to the polarization of electromagnetic fields, the relationship between the rank of the multistatic matrix and the number of small scatterers is different from that associated with the scalar wave. Multiple scattering between scatterers is considered, and the inverse scattering problem of determining the polarization tensors is nonlinear, which, however, is solved by the proposed analytical approach where no associated forward problem is iteratively evaluated.

A robust noniterative method for obtaining scattering strengths of multiply scattering point targets

A noniterative method based on the least squares technique is presented in this letter to obtain the scattering strengths of multiply scattering point targets. Benefiting from the least squares' optimization property, this new method achieves a good estimation of the scattering strengths. Compared with the noniterative method proposed in a recent paper [E. A. Marengo and F. K. Gruber "Noniterative analytical formula for inverse scattering of multiply scattering point targets," J. Acoust. Soc. Am. 120, 3782-3788 (2006)], the new method produces more accurate results in the presence of noise.

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 "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.