Purpose: A human observer study was performed for a signal detection task for the case of fan-beam x-ray computed tomography. Hotelling observer (HO) performance was calculated for the same detection task without the use of efficient channels. By considering the full image covariance produced by the filtered backprojection (FBP) algorithm and avoiding the use of channels in the computation of HO performance, the authors establish an absolute upper bound on signal detectability. Therefore, this study serves as a baseline for relating human and ideal observer performance in the case of fan-beam CT.
Methods: Eight human observers participated in a two-alternative forced choice experiment where the signal of interest was a small simulated ellipsoid in the presence of independent, identically distributed Gaussian detector noise. Theoretical performance of the HO, which is equivalent to the ideal observer in this case (see Sec. 13.2.12 in Barrett and Myers [Foundations of Image Science (Wiley, Hoboken, NJ, 2004)], was also computed and compared to the performance of the human observers. In addition to a reference FBP implementation, two FBP implementations with inherent loss of HO signal detectability (e.g., by apodizing the ramp filter) were also investigated. Each of these latter two implementations takes the form of a discrete-to-discrete linear operator (i.e., a matrix), which has a nontrivial null-space resulting in the loss of detectability.
Results: Estimated observer detectability index (d(A)) values for the human observers and SNR values for the HO were obtained. While Hanning filtering in the FBP implementation with a cutoff frequency of 1/4 of the Nyquist frequency reduces HO SNR (due to the reconstruction matrix's nontrivial null-space), this filtering was shown to consistently improve human observer performance. By contrast, increasing the image pixel size was seen to have a comparable effect on both the HO and the human observers, degrading performance.
Conclusions: These results, which characterize HO and human observer performance for a signal detection task in fan-beam FBP noise, form a basis for applying model observer metrics to fan-beam CT when knowledge of the full image-domain noise statistics is important. Further, by calculating HO performance without relying on channels, these results are particularly relevant when an information theoretic approach is considered, e.g., in optimization of the image reconstruction algorithm with respect to preservation of signal detectability. Finally, the HO (which is here equivalent to the ideal observer) provides an absolute upper bound on detection performance, and our results therefore provide insight into the performance of human observers relative to the optimum for two different cases wherein ideal observer performance is compromised through degradation of the data quality. In one case (regularization), human performance is improved to practically ideal performance, and in the other (larger pixel size), ideal and human observer performance are approximately degraded equivalently.