Task‐based weights for photon counting spectral x‐ray imaging

Abstract

To develop a framework for taking the spatial frequency composition of an imaging task into account when determining optimal bin weight factors for photon counting energy sensitive x-ray systems. A second purpose of the investigation is to evaluate the possible improvement compared to using pixel based weights. The Fourier based approach of imaging performance and detectability index d' is applied to pulse height discriminating photon counting systems. The dependency of d' on the bin weight factors is made explicit, taking into account both differences in signal and noise transfer characteristics across bins and the spatial frequency dependency of interbin correlations from reabsorbed scatter. Using a simplified model of a specific silicon detector, d' values for a high and a low frequency imaging task are determined for optimal weights and compared to pixel based weights. The method successfully identifies bins where a large point spread function degrades detection of high spatial frequency targets. The method is also successful in determining how to downweigh highly correlated bins. Quantitative predictions for the simplified silicon detector model indicate that improvements in the detectability index when applying task-based weights instead of pixel based weights are small for high frequency targets, but could be in excess of 10% for low frequency tasks where scatter-induced correlation otherwise degrade detectability. The proposed method makes the spatial frequency dependency of complex correlation structures between bins and their effect on the system detective quantum efficiency easier to analyze and allows optimizing bin weights for given imaging tasks. A potential increase in detectability of double digit percents in silicon detector systems operated at typical CT energies (100 kVp) merits further evaluation on a real system. The method is noted to be of higher relevance for silicon detectors than for cadmium (zink) telluride detectors.