Statistical radar imaging of diffuse and specular targets using an expectation-maximization algorithm

Radar imaging is often posed as a problem of estimating deterministic reflectances observed through a linear mapping and additive Gaussian receiver noise. We consider an alternative view which considers the reflectances themselves to be a realization of a random process; imaging then involves estimating the parameters of that underlying process. Purely diffuse radar targets are modeled by a zero-mean Gaussian process, while specular targets introduce an additive component with fixed amplitude and random uniform phase. When conventional stepped frequency waveforms are employed, the linear mapping amounts to a Fourier transform, and parameter estimation is straightforward. If more complicated waveforms are employed, maximum-likelihood parameter estimates cannot be readily computed analytically; hence, we explore an iterative expectation-maximization algorithm proposed by Snyder, O’Sullivan, and Miller. Although this algorithm was designed for diffuse radar imaging, arguments based on the central limit theorem and computational experiments support its applicability to the specular case. The resulting estimates tend to be unacceptably rough due to the ill-posed nature of maximum-likelihood estimation of functions from limited data, so some kind of regularization is needed. We explore penalized likelihoods based on entropy functionals, a roughness penalty proposed by Silverman, and an information-theoretic formulation of Good’s roughness penalty.