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Imaging below the diffraction limit: a statistical analysis

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2 Author(s)
Shahram, M. ; Dept. of Electr. Eng., Univ. of California, Santa Cruz, CA, USA ; Milanfar, P.

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 Crame´r-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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Image Processing, IEEE Transactions on  (Volume:13 ,  Issue: 5 )