Abstract

The fractional correlation is a new operation that can easily be implemented by optical means. This operation might be useful for shift-variant pattern recognition and for image restoration. The Wiener filter is the optimal filter according to the minimal square-error criterion. For a given spectral noise that distorts the reference image, this filter is optimal for restoring an image in noise. A fractional Wiener filter is suggested for restoring reference objects in a fractional correlation system. The new filter sometimes performs better than the conventional Wiener filter.

© 1996 Optical Society of America

New interpretations of Wiener filters for image recognition

Emanuel Marom and Hanni Inbar
J. Opt. Soc. Am. A 13(7) 1325-1330 (1996)

Fractional correlation operation: performance analysis

Yigal Bitran, Zeev Zalevsky, David Mendlovic, and Rainer G. Dorsch
Appl. Opt. 35(2) 297-303 (1996)

Fractional Radon transform: definition

Zeev Zalevsky and David Mendlovic
Appl. Opt. 35(23) 4628-4631 (1996)

Optimum piecewise-constant Wiener filters

Leonard J. Cimini and Saleem A. Kassam
J. Opt. Soc. Am. 71(10) 1162-1171 (1981)

Space-variant simultaneous detection of several objects by the use of multiple anamorphic fractional-Fourier-transform filters

Javier García, David Mendlovic, Zeev Zalevsky, and Adolf Lohmann
Appl. Opt. 35(20) 3945-3952 (1996)