<title>Digital Processing Of Images In Speckle Noise</title>

Abstract

Abstract Digital filtering techniques for speckle reduction are studied using several conventional filters and homomorphic filters. It is shown that homomorphic filtering has higher resolu­ tion than straightforward linear filtering. Among the several filters considered, the homo­ morphic Wiener filter is found to yield the best results. Examples and possible extensions of these results are discussed.IntroductionIn an earlier study, a digital model of fully developed speckle was implemented and verified by comparing optical and digital speckle images. The model was also used to obtain detection probabilities of targets imaged in the presence of speckle . 3'4 For an object with intensity u(x,y), its image in the presence of speckle is given byv(x,y) = u(x,y) s(x,y) (1)where s(x,y) represents the speckle intensity. For each x,y, the speckle noise s(x,y) is a random variable with a single sided (s > 0) exponential probability density. For sampled images, if the sampling distance is equal to the correlation distance of the speckle, then x and y can be assumed to take integer values on a rectangular grid and s(x,y) is a spatially uncorrelated random field on this grid. Often, several independent looks of the object can be obtained and we havevR(x,y) = u(x,y) sR(x,y), K = 1,..., N (2)re s^(x,y) is the Kindependent exponen that the N-look averagewhere K sample function of the speckle random field. Since {s«.;K = lf. .., N} are exponentially distributed random variables, it is a simple matter to showi l~i N= - I