Photon Counting Computed Tomography Image Restoration via Mixture Gaussian Noise Model: Initial Study

Photon counting computed tomography (PCCT) can offer substantial benefits over conventional energy-integrating CT due to its high-speed semiconductors. However, the PCCT splits the transmitted spectrum into multiple bins, leading to a relatively low signal-to-noise ratio in each energy bin and then the reconstructed PCCT images suffer from noise. Most of existing PCCT image restoration methods assume that the noise in the PCCT images is independent and identically distributed (i.i.d). This might produce bias in the results because the noise distribution is much more complicated. In this work, we model the noise in the PCCT image via i.i.d mixture of Gaussian (MOG) noise assumption, which can successfully characterize various shape in the PCCT images. Then the i.i.d MOG model is introduced into a PCCT image restoration approach. The prior information (an average image from the PCCT images at multiple bins) is added to the restoration approach to further promote performance. Therefore, the presented restoration approach can be termed as "pMOG". Then, an effective optimization algorithm is designed to solve the presented pMOG approach. The experimental results with simulation study demonstrate that the presented pMOG approach can effectively suppress noise and preserve resolution compared to the non-local means approach.