OPTIMUM, NON-LINEAR PROCESSING OF NOISY IMAGES

QC 351 A7 no. 23It has been traditional to constrain image processing to linear operations upon the image. This is a realistic limitation of analog processing. In this paper, the calculus of variations is used to find the optimum, generally non - linear, processor of a noisy image. In general, such processing requires the use of an electronic computer. The criterion of optimization is that expectation (10. - (5j1K) be a minimum. Subscript j denotes the spatial frequency w. at which the unknown object spectrum 0 is to be re- stored, 0 denotes the optimum restoration by this criterion, and K is an even power at the user's discretion. A further generality is to allow the image- forming phenomenon to obey an arbitrary law I. = L(T., O., N.). Here, J J J T. denotes the intrinsic system characteristic (usually the optical transfer function), and N. represents a noise function. The optimum Oj is found to be the root of a finite polynomial. When the particular value K = 2 is used, the root O. is known analytically, along with the expected, mean -square, minimal error due to its use. When K = 2, processor O. has the added significance of minimizing the total mean -square restoration error over the spatial object. This error may be further minimized by choice of an optimal processing bandwidth. Particular processors O. are found for the "image recognition" problem and for the case of a "white" object region. The latter case is numerically simulated.This title from the Optical Sciences Technical Reports collection is made available by the College of Optical Sciences and the University Libraries, The University of Arizona. If you have questions about titles in this collection, please contact repository@u.library.arizona.edu