Adaptive interferometric imaging in clutter and optimal illumination

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. (Some figures in this article are in colour only in the electronic version)