Likelihood-based bilateral filtration in material decomposition for photon counting CT

The maximum likelihood (ML) principle has been a gold standard for estimating basis line-integrals due to the optimal statistical property. However, the estimates are sensitive to noise from large attenuations or low dose levels. One may apply filtering in the estimated basis sinograms or model-based iterative reconstruction. Both methods effectively reduce noise, but the degraded spatial resolution is a concern. In this study, we propose a likelihood-based bilateral filter (LBF) for the estimated basis sinograms to reduce noise while preserving spatial resolution. It is a post-processing filtration applied to the ML-based basis line-integrals, the estimates with a high noise level but minimal degradation of spatial resolution. The proposed filter considers likelihood in neighbours instead of weighting by pixel values as in the original bilateral filtration. Two-material decomposition (water and bone) results demonstrate that the proposed method shows improved noise-to-spatial resolution tendency compared to conventional methods.