Radiographic Image Enhancement by Wiener Decorrelation

Abstract

The primary foeus of the applieation of image proeessing to radiography is the problem of segmentation. The general segmentation problem has been attaeked on a broad front [1,2], and thresholding, in partieular, is a popular method [1,[3][4][5][6]. Unfortunately, geometrie unsharpness destroys the erisp edges needed for unambiguous deeisions, and this diffieulty ean be eonsidered a problem in filtering in whieh the objeet is to devise a high-pass (sharpening) filter.This approach has been studied for more than 20 years [7][8][9][10][11][12][13].The inverse filter ean be devised either in the spatial domain or the frequeney domain.Both eases require either a model of the degradation proeess (geometrie unsharpness), or a set of "ideal" image/degraded image pairs from whieh an inverse filter ean be ealeulated by some estimation method (such as least squares).In the ease of radiography with an ineoherent source, a simple model of the imaging proeess leading to a frequeney domain solution ean be developed.The remainder of this paper deseribes a model of the radiographie proeess and the eonsequenees of eertain eonditions and simplifying assumptions. A partieular method of inverse filtering (Wiener filtering) is applied to some digitized radiographs and the results are diseussed. IMAGING PROCESSThe formation of radiographie images on a plane loeated at z be shown [14] to be a superposition integral of the formwhere u, v, and ware the direetion eosines with respeet to the X-, y-, and z-axes, P(x',y') is the intensity of an isotropie souree at z = 0, ft(x", y" z") is the attenuation eoeffieient along the ray from