RECONSTRUCTING BINARY POLYGONAL OBJECTS FROM PROJECTIONS - A STATISTICAL VIEW

In many applications of tomography, the fundamental quantities of inte rest in an image are geometric ones. In these instances, pixel-based s ignal processing and reconstruction is at best inefficient, and, at wo rst, nonrobust in its use of the available tomographic data. Classical reconstruction techniques such as filtered back-projection tend to pr oduce spurious features when data is sparse and noisy; these ''ghosts' ' further complicate the process of extracting what is often a limited number of rather simple geometric features. In this paper, we present a framework that, in its most general form, is a statistically optima l technique for the extraction of specific geometric features of objec ts directly from the noisy projection data. We focus on the tomographi c reconstruction of binary polygonal objects from sparse and noisy dat a. In our setting, the tomographic reconstruction problem is essential ly formulated as a (finite-dimensional) parameter estimation problem. In particular, the vertices of binary polygons are used as their defin ing parameters. Under the assumption that the projection data are corr upted by Gaussian white noise, we use the maximum likelihood (ML) crit erion, when the number of parameters is assumed known, and the minimum description length (MDL) criterion for reconstruction when the number of parameters is not known. The resulting optimization problems are n onlinear and thus are plagued by numerous extraneous local extrema, ma king their solution far from trivial. In particular, proper initializa tion of any iterative technique is essential for good performance. To this end, we provide a novel method to construct a reliable yet simple initial guess for the solution. This procedure is based on the estima ted moments of the object, which may be conveniently obtained directly from the noisy projection data. (C) 1994 Academic Press, Inc.