Purpose : Material decomposition induces substantial noise in basis images and their synthesized computed tomography (CT) images. A likelihood-based bilateral filter was previously developed as a neighborhood filter that effectively reduces noise. However, this method is sensitive to image contrast, and the noise texture needs improvement. It is also necessary to address how to optimally combine filtered basis images to synthesize CT images. This study addressed these issues by introducing total likelihood and a noise-matched condition. Methods: The experimental feasibility of the proposed method was demonstrated in a benchtop photon- counting CT (PCCT) system using the following steps: (1) A calibration process for forward modeling, (2) maximum likelihood (ML)-based material decomposition, which is accurate but suffers from substantial noise, (3) noise reduction by applying a total-likelihood-based filter, and (4) CT image synthesis using the noise- matched condition. The proposed method was compared with conventional neighborhood filters and statistical iterative reconstruction with edge-preserving regularization. Results: The local noise and task-based modulation transfer function (TTF) were analyzed using a test phantom, and the proposed method was found to preserve the spatial resolution better than the other methods, especially in low-contrast regions. In the chicken leg experiment, the proposed method improved the fine structures and background textures in the denoised images and exhibited superior properties in analyzing the noise power spectrum. Conclusion: The proposed method is effective and computationally efficient for noise reduction in PCCT and can potentially replace conventional iterative edge-preserved regularization approaches.
