We i n troduce an output least-squares method for impedance tomography problems that have regions of high conductivity surrounded by regions of lower conductivity. The high conductivity is modeled on network approximation results from an asymptotic analysis and its recovery is based on this model. The smoothly varying part of the conductivity is recovered by a linearization process as is usual. We present the results of several numerical experiments that illustrate the performance of the method.

We present a general method for estimating the location of small, well-separated scatterers in a randomly inhomogeneous environment using an active sensor array. The main features of this method are (i) an arrival time analysis of the echo received from the scatterers, (ii) a singular value decomposition of the array response matrix in the frequency domain, and (iii) the construction of an objective function in the time domain that is statistically stable and peaks on the scatterers. By statistically stable we mean here that the objective function is self-averaging over individual realizations of the medium. This is a new approach to array imaging that is motivated by time reversal in random media, analyzed in detail previously. It combines features from seismic imaging like arrival time analysis with frequency-domain signal subspace methodology like MUltiple SIgnal Classification (MUSIC). We illustrate the theory with numerical simulations for ultrasound.

A frequently used broadband array imaging method is Kirchhoff or travel time migration. In smooth and known media Kirchhoff migration works quite well, with range resolution proportional to the reciprocal of the bandwidth and cross range resolution that is proportional to the reciprocal of the array size. In a randomly inhomogeneous medium, Kirchhoff migration is unreliable because the images depend on the detailed scattering properties of the random medium that are not known. In Borcea et al (2005 Interferometric array imaging in clutter Inverse Problems 21 1419–60) we introduced an imaging functional that does not depend on the detailed properties of the random medium, that is, it is statistically stable. This is the coherent interferometric (CINT) imaging functional, which can be viewed as a smoothed version of Kirchhoff migration. Smoothing increases the statistical stability of the image but causes blurring. In this paper, we introduce an adaptive version of CINT in which there is an optimal trade-off between statistical stability and blurring. We also introduce optimal illumination schemes for achieving the best possible resolution of the images obtained with CINT.

We introduce a space-time interferometric array imaging functional that provides statistically stable images in cluttered environments. We also present a resolution theory for this imaging functional that relates the spacetime coherence of the data to the range and cross-range resolution of the image. Extensive numerical simulations illustrate the theory and address some implementation issues.