Log conversion with fewer counts for photon counting CT: decreasing both bias and variance simultaneously

Photon counting detector (PCD)-based computed tomography (CT) has demonstrated significant clinical potentials, especially for low-dose applications. However, its effectiveness is compromised at extremely low photon counts as the detector pixel area decreases significantly compared to conventional energy-integrating detectors (EIDs). During the logarithmic transformation process, the increased presence of “zero count” in Poisson data complicates the process. Conventional solutions, such as zero-replacement, introduce an artificial positive value to replace zero. However, the added value skews Poisson statistics and creates additional bias and noise, leading to inaccurate CT numbers. Previous studies have identified correction methods that reduce bias; however, this reduction is usually achieved at the expense of increased noise. In this study, we present a novel method that optimizes the trade-off between bias and noise in post-log data, enhancing accuracy and repeatability of low-dose CT imaging. The proposed method introduces count-dependent terms to independently address bias and variance. Computer simulations were conducted to assess the performance of the proposed method. Results demonstrated reductions in post-log bias and variance compared to traditional methods. Specifically, the proposed method achieved 55.83% reduction in bias and 63.86% reduction in variance within the sinogram domain on average compared to other methods implemented in this study. Additionally, on average, reconstructed images showed 35.0% reduction in root mean square error (RMSE) and 62.7% improvements in contrast-to- noise ratio (CNR) among all methods, indicating enhanced CT number accuracy and image contrast. By mitigating issues associated with low photon counts, the proposed correction method enhances clinical viability of low-dose PCD-CT, facilitating more accurate quantification and diagnosis.