Reconstruction from projections based on detection and estimation of objects

This paper considers the problem of observing a 2D function via its 1D projections (Radon transform); it presents a framework for detecting, locating and describing objects contained within a 2D cross-section by using noisy measurements of the Radon transform directly, rather than post-processing a reconstructed image. This framework offers the potential for significant improvements in applications where (1) attempts to perform an initial inversion with insufficient measurement data result in severely degraded reconstructions, and (2) the ultimate goal of the process is to obtain several specific pieces of information about the cross-section. To illustrate this perspective, we focus our attention on the problem of obtaining maximum-likelihood (ML) estimates of the parameters characterizing a single random object situated within a deterministic background medium, and we investigate the performance, robustness, and computational structure of the ML estimation procedure.