5 January 2004 Statistical analysis of achievable resolution in incoherent imaging
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Abstract
The present paper concerns the statistical analysis of limits to achievable resolution in a so-called "diffraction-limited" imaging system. The canonical case study is that of incoherent imaging of two closely-spaced sources of possibly unequal intensities. The objective is to study how far beyond the classical Rayleigh limit of resolution one can reach at a given signal to noise ratio. We consider the definition of resolution limit from a statistical point of view as the ability of the imaging system to distinguish two closely-located sources in presence of additive noise. This problem can be stated in a hypothesis testing framework where the hypotheses consider whether one or two point sources are present. In terms of signal detection/ estimation, this leads to composite detection/estimation problem where a deterministic signal with unknown parameters is being sought. To solve this problem, we use locally optimal statistical tests with respect to a desired range of (small) separations between the point sources. Specifically, we will derive explicit relationships between the minimum detectable distance between two point sources, and the required SNR. For a specific point spread function, the required SNR can be expressed as a function of probabilities of detection and false alarm and the distance between point sources.
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Morteza Shahram, Morteza Shahram, Peyman Milanfar, Peyman Milanfar, "Statistical analysis of achievable resolution in incoherent imaging", Proc. SPIE 5204, Signal and Data Processing of Small Targets 2003, (5 January 2004); doi: 10.1117/12.505150; https://doi.org/10.1117/12.505150
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