Optimality of nonlinear joint transform correlation in the context of the statistical estimation theory

Philippe Refregier

doi:10.1117/12.326788

9 October 1998 Optimality of nonlinear joint transform correlation in the context of the statistical estimation theory

Philippe Refregier

Proceedings Volume 3466, Algorithms, Devices, and Systems for Optical Information Processing II; (1998) https://doi.org/10.1117/12.326788
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1998, San Diego, CA, United States

Abstract

Nonlinear joint transform correlators (JTCs) have been proposed for optical information processing. They have been shown to be attractive in many difficult instances because of their high discriminating performance. However, unlike the linear matched filter, which was designed on the basis of the statistical estimation theory before its implementation in optical correlators, investigations on nonlinear filtering techniques have been mostly experimental and their basic properties in terms of signal processing and pattern recognition still need theoretical analyses. We propose in this paper to analyze the optimal solutions obtained in the context of the statistical estimation theory when the spectral density of the additive Gaussian noise is unknown. Maximum likelihood, maximum a posteriori and Bayesian solutions to this problem are discussed and practical consequences are analyzed. In particular, we show that nonlinear JTC methods can be considered as a first order, but very efficient, approximation of these optimal solutions.

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Philippe Refregier "Optimality of nonlinear joint transform correlation in the context of the statistical estimation theory", Proc. SPIE 3466, Algorithms, Devices, and Systems for Optical Information Processing II, (9 October 1998); https://doi.org/10.1117/12.326788

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KEYWORDS

Joint transforms

Statistical analysis

Estimation theory

Fourier transforms

Nonlinear filtering

Optical correlators

Filtering (signal processing)

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