Optimal weighting strategies for maximizing contrast-to-noise ratio in photon counting CT images

Photon counting detectors (PCDs) with energy discrimination capabilities enable spectral imaging and provide higher contrast-to-noise ratio (CNR) than energy integrating detectors (EIDs). Previous work has shown that optimal weighting strategies can further improve CNR. However, a systematic comparison of different weighting strategies and their maximum achievable CNR has not been investigated. In this work, we derive the analytical expressions of the maximum achievable CNR using pre-log optimal weights, post-log optimal weights, and optimal virtual monoenergetic (VM) weights for realistic PCD energy responses and imaging tasks. We compare the CNR performance of these weighting strategies using simulated phantoms and a physical phantom scan for low-contrast tasks. Our results show that for spectral tasks, pre-log optimal weights, post-log optimal weights, and optimal VM weights achieve approximately equal maximum CNR (to within 2% of each other) and outperform total count (TC)