SIMULATED ANNEALING AND ESTIMATION THEORY IN CODED-APERTURE IMAGING (RECONSTRUCTION, MONTE CARLO, WIENER FILTER).

Abstract

Coded-aperture imaging without detector motion can be used to reconstruct three-dimensional radionuclide distributions in the context of nuclear medicine. This approach offers several advantages over the rotating gamma-ray camera systems presently employed in the clinic. These advantages include improved sensitivity, potentially better spatial resolution, and the capability of doing dynamic studies. There are two problems associated with the coded-aperture approach, however. First, the data is "multiplexed", which refers to the fact that many line integrals of the source distribution are combined together and not measured individually, so that information is lost. Second, the number of resolvable detector elements is typically an order of magnitude less than the number of object elements to be reconstructed, so that the reconstruction problem is underdetermined. Consequently, the reconstruction is not unique. By using various types of a priori information in forming the reconstruction, however, it is possible to augment the incomplete data set. Two algorithms are presented to reconstruct objects from their coded-image projections and various types of a priori information. The first, a Monte Carlo algorithm, is a flexible and computationally efficient approach using the a priori knowledge of positivity and nearest-neighbor correlation. This algorithm is used to qualitatively explore the effect of the data-taking geometry on reconstruction performance. The second algorithm is a linear estimator incorporating as a priori knowledge completely general first- and second-order statistical information about the object class to be reconstructed. The linear-estimator formalism also provides a minimum-variance expression for system optimization. This linear algorithm is used to explore the effects of correct and incorrect a priori information on reconstruction performance, and to quantitatively investigate reconstruction quality with respect to data-taking geometry.