Multiscale Signal Processing and Shape Analysis for an Inverse SAR Imaging System

Abstract

The great challenge in signal processing is to devise computationally efficient and statistically optimal algorithms for estimating signals from noisy background and understanding their contents. This thesis treats the problem of multiscale signal processing and shape analysis for an Inverse Synthetic Aperture Radar (ISAR) imaging system. To address some of the limitations of conventional techniques in radar image processing, an information theoretic approach for target motion estimation is first proposed. A wavelet based multiscale method for shape enhancement is subsequently derived and followed by a regression technique for shape recognition.Building on entropy-based divergence measures which have shown promising results in many areas of engineering and image processing, we introduce in this thesis a new generalized divergence measure, namely the Jensen-Rényi divergence. Upon establishing its properties such as convexity and its upper bound etc., we apply it to image registration for ISAR focusing as well as related problems in data fusion. Attempting to extend current approaches to signal estimation in a wavelet framework, which have generally relied on the assumption of normally distributed perturbations, we propose a novel non-linear filtering technique, as a pre-processing step for the shapes obtained from an ISAR imaging system. The key idea is to project a noisy shape onto a wavelet domain and to suppress wavelet coefficients by a mask derived from curvature extrema in its scale space representation. For a piecewise smooth signal, it can be shown that filtering by this curvature mask is equivalent to preserving the signal pointwise Hölder exponents at the singular points, and to lifting its smoothness at all the remaining points. To identify a shape independently of its registration information, we propose matching two configurations by regression, using notations of general shape spaces and procrustean distances. In particular, we study the generalized matching by estimating mean shapes in two dimensions. Simulation results show that matching by way of a mean shape is more robust than matching target shapes directly.