Signal detection theory and reconstruction algorithms--performance for images in noise

In many noisy image processing situations, decision making is the ultimate objective. In this paper, we show using signal detection theory how direct optimal processing of the projection data yields a considerable gain in the decision making performance over that obtained by first using image reconstruction. The problem is formulated in the framework of a two hypotheses detection problem. Optimal processors based on the likelihood ratio approach have been presented for two cases. The first considers direct processing of the projection data. The second applies optimal decision theory to the reconstructed data. Results based on computer simulation are presented in the form of receiver operating curves (ROCs) for different signal-to-noise (SNR) ratios. Early results indicate that large performance gains can be achieved by direct optimal processing of the projection data compared with optimal processing of reconstructed data. Results for the latter case can be interpreted as providing an upper bound on all postreconstruction decision rules. We hope to extend this approach to a number of different aspects of the image decision making problem.