Statistical and information-theoretic analysis of resolution in imaging and array processing

This work investigates some detection-theoretic, estimation-theoretic and information-theoretic methods to analyze the problem of determining resolution limits in imaging systems. The canonical case study is formulated based on a model of the blurred image of two closely-spaced point sources of unknown brightness. To quantify a measure of resolution in statistical terms, we address the following question: What is the minimum detectable separation between two point sources at a given signal-to-noise ratio (SNR), and for pre-specified probabilities of detection and false alarm?". Furthermore, asymptotic performance analysis for the estimation of the unknown parameters is carried out using the Cramer-Rao bound. Also, we analyze the problem of resolution by computing the Kullback-Leibler distance to further confirm the earlier results and to establish a link between the detection-theoretic approach and Fisher information. To study the effects of variation in point spread function (PSF) and model mismatch, we present a perturbation analysis of the detection problem as well. The proposed analysis methodologies presented are carried out for the general two-dimensional model and general sampling scheme. We consider different sampling scenarios and in particular study the case of under-Nyquist (aliased) images.; The approach we have advocated for determining resolution limits in imaging can be similarly used to develop statistical algorithms and performance limits for resolving sinusoids with nearby frequencies, in the presence of noise. Here the problem is that of distinguishing whether the received signal is a single-frequency sinusoid or a double-frequency sinusoid. We derive a locally optimal detection strategy that can be applied in a stand-alone fashion or as a refinement step for existing spectral estimation methods, to yield improved performance.