Abstract

An arbitrary image, when considered as a matrix, can be expressed as a weighted sum of rank 1 (outer product) matrices. The singular value decomposition of a matrix leads to a compact representation of an image that is optimum in the least squares sense. In this paper we combine the general concept of a truncated outer product expansion of a reference image with optical correlators. We investigated analytically and via computer simulations the effects of the truncation on the auto and cross correlations and sidelobes. Since the outer product expansion can be easily implemented optically by using orthogonally oriented 1-D spatial light modulators, this technique has the potential of eliminating the requirement of 2-D devices for representing the reference function in an optical correlator. Additionally, the truncated outer product expansion of the reference function can potentially lead to an order of magnitude reduction in the data storage requirements. Optical architectures for combining the outer product processor with an optical image correlator will be described.

© 1992 Optical Society of America