We analyze the performance of the Fourier plane nonlinear filters in terms of signal-to-noise ratio (SNR). We obtain a range of nonlinearities for which SNR is robust to the variations in input-noise bandwidth. This is shown both by analytical estimates of the SNR for nonlinear filters and by experimental simulations. Specifically, we analyze the SNR when Fourier plane nonlinearity is applied to the input signal. Using the Karhunen–Loève series expansion of the noise process, we obtain precise analytic expressions of the SNR for Fourier plane nonlinear filters in the presence of various types of additive-noise processes. We find a range of nonlinearities that need to be applied that keep the output SNR of the filter stable relative to changes in the noise bandwidth.
© 2001 Optical Society of America
(100.5010) Image processing : Pattern recognition
Original Manuscript: June 26, 2000
Revised Manuscript: November 27, 2000
Manuscript Accepted: November 27, 2000
Published: September 1, 2001
Nasser Towghi, Luting Pan, and Bahram Javidi, "Noise robustness of nonlinear filters for image recognition," J. Opt. Soc. Am. A 18, 2054-2071 (2001)