Analysis of observer performance in unknown-location tasks for tomographic image reconstruction

Abstract

Our goal is to optimize regularized image reconstruction for emission tomography with respect to lesion detectability in the reconstructed images. We consider model observers whose decision variable is the maximum value of a local test statistic within a search area. Previous approaches have used simulations to evaluate the performance of such observers. We propose an alternative approach, where approximations of tail probabilities for the maximum of correlated Gaussian random fields facilitate analytical evaluation of detection performance. We illustrate how these approximations, which are reasonably accurate at low probability of false alarm operating points, can be used to optimize regularization with respect to lesion detectability.

Fig. 1

PSfrag replacements. Mean background f̄_b with the target signal f_s superimposed (a) and a profile through them (b). The largest of the search areas considered (diameter of 23 pixels) is indicated as a black circle in (a).

Fig. 2

Detection performance of MaCPPW observers versus QPWLS reconstruction resolution: P_D obtained analytically (a), P_D obtained empirically (b), and AUC obtained empirically (c). Results are shown for five different degrees of prewhitening accuracy. The search area is a disk with a diameter of 9 pixels.

Fig. 3

QPWLS resolution that maximizes the P_D (obtained analytically and empirically) or AUC (obtained empirically) versus search area diameter (a). AUC improvement with optimally regularized QPWLS over unregularized WLS versus search area diameter (b). Results are shown for the MaCNPW observer.

Fig. 4

QPWLS reconstructions of a noisy Poisson data set with a resolution of 3 pixels (a), 4 pixels (b), or 5 pixels (c), and profiles through the three images (d). The signal is present in the center of the search area.

Fig. 5

Empirical and analytical probabilities of false alarm and detection for the MaCNPW observer with a search area diameter of 7 pixels [(a)–(c)] and 15 pixels [(d)–(f)]. The plots show the P_FA versus detection threshold [(a),(d)], the P_D versus detection threshold [(b),(e)], and the P_D (with error bars) versus QPWLS resolution for a fixed P_FA=0.02 [(c),(f)]. (The error bars are small enough to fit in the plot markers.)