IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Statistical and Information-Theoretic Analysis of Resolution in Imaging

  • Feb. 10, 2009
  • 3:30 p.m.
  • Sumwalt 102


This work investigates some statistical 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.

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