Abstract

Characteristics of the random walk point spread function (psf) consisting of a set of N impulses randomly distributed within a pre scribed region in space and the associated transfer function are presented. We show that the effect of the multiple point psf is similar to that of a low pass filter having a peak value proportional to N² and an asymptotic value proportional to N at high spatial frequencies. The occurrence of zeros in the transfer function is also considered. A statistical argument is used to demonstrate that the zeros for this special transfer function present little difficulty in recovering images blurred by the random walk psf. This result is verified numerically, and we present a table summarizing the number of zeros per unit area for several common blur functions. The effects of the number of impulses and their spatial distributions on the occurrence of zeros is also considered. The relatively few number of zeros in the transfer function permits high fidelity reconstructions to be obtained by using a modified inverse filter. Several images are coded and recovered to show the general applicability of the method. Additionally, the low pass nature of the blur function allows improved compression ratios to be achieved by using the coded image, as compared to the original scene. We describe the noise using a quality factor to characterize the decompressed and decoded images. Excellent recovery is obtained.

© 1992 Optical Society of America