Estimation of object location from wideband scattering data

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.

Higher-order (nonlinear) diffraction tomography: reconstruction algorithms and computer simulation

The usual propagation transform of diffraction tomography is generalized into higher-order (nonlinear) propagation transforms via use of the Born series as the data-generating model in scattering experiments. Nonlinear tomographic reconstruction algorithms are developed for inversion of scattered field data modeled up to an arbitrarily large (possibly infinite) number of terms in the Born series. A computer simulation study is included to illustrate the performance of the algorithms for the case of scattering objects with cylindrical symmetry.

A new reconstruction approach for reflection mode diffraction tomography

Reflection mode diffraction tomography (RM DT) is an inversion scheme used to reconstruct the acoustical refractive index distribution of a scattering object. In this work, we reveal the existence of statistically complementary information inherent in the backscattered data and propose reconstruction algorithms that exploit this information for achieving a bias-free reduction of image variance in RM DT images. Such a reduction of image variance can potentially enhance the detectability of subtle image features when the signal-to-noise ratio of the measured scattered data is low in RM DT. The proposed reconstruction algorithms are mathematically identical, but they propagate noise and numerical errors differently. We investigate theoretically, and validate numerically, the noise properties of images reconstructed using one of the reconstruction algorithms for several different multifrequency sources and uncorrelated data noise.