期刊
IEEE TRANSACTIONS ON IMAGE PROCESSING
卷 13, 期 5, 页码 677-689出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIP.2004.826096
关键词
Cramer-Rao bound; diffraction; estimation; hypothesis test; imaging; Rayleigh limit; resolution; super-resolution
The present paper is concerned with the statistical analysis of the resolution limit 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 brightness. The objective is to study how far beyond the classical Rayleigh limit of resolution one can reach at a given signal to noise ratio. The analysis uses tools from statistical detection and estimation theory. Specifically, we will derive explicit relationships between the minimum detectable distance between two closely-spaced point sources imaged incoherently at a given SNR. For completeness, asymptotic performance analysis for the estimation of the unknown parameters is carried out using the Cramer-Rao bound. To gain maximum intuition, the analysis is carried out in one dimension, but can be well extended to the two-dimensional case and to more practical models.
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