Statistical Signal Processing Methods in Scattering and Imaging

This Ph.D. dissertation addresses two related topics in wave-based signal processing: 1) Cramer-Rao bound (CRB) analysis of scattering systems formed by pointlike scatter-ers in one-dimensional (1D) and three-dimensional (3D) spaces. 2) Compressive optical coherent imaging, based on the incorporation of sparsity priors in the reconstructions. The first topic addresses for wave scattering systems in 1D and 3D spaces the infor-mation content about scattering parameters, in particular, the targets ’ positions and strengths, and derived quantities, that is contained in scattering data corresponding to reflective, transmissive, and more general sensing modalities. This part of the dis-sertation derives the Cramer-Rao bound (CRB) for the estimation of parameters of scalar wave scattering systems formed by point scatterers. The results shed light on the fundamental difference between the approximate Born approximation model for weak scatterers and the more general multiple scattering model, and facilitate the iden-tification of regions in parameter space where multiple scattering facilitates or obstructs the estimation of parameters from scattering data, as well as of sensing configuration