Statistical Iteration Reconstruction based on Gaussian Mixture Model for Photon-counting CT

Photon-counting computed tomography (PCCT) can simultaneously obtain multi-energy data with abundant energy-dependent material-specific information of the scanned object. However, the photon counts in each energy bin are decreased and the collected data suffers from photon starvation effects, which degrades the quality of the reconstructed PCCT images. To solve it, many statistical iteration reconstruction (SIR) methods have been proposed by constructing data-fidelity and prior information terms to suppress noise and remove artifacts. However, most of the current SIR methods assume the noise in PCCT images follows a Gaussian distribution, which deviates the real distribution of the noise in PCCT images. Therefore, we propose a new statistical iteration reconstruction method by considering more complex noise distribution in reality. Specifically, Gaussian mixture model (GMM), which is a universal approximator for any continuous density function, is utilized to model the noise in PCCT images. Moreover, the multi-energy PCCT images are treated as a 3-order tensor which is regularized by three dimensional total variation (3DTV) prior term. Finally, a statistical iteration reconstruction model based on GMM and 3DTV is established for PCCT imaging. For shorten, we call the presented reconstruction model as “GMM-3DTV”. We then develop an expectation-maximization (EM) algorithm to solve the presented GMM-3DTV method. Numerical studies demonstrate the improvements of the presented GMM-3DTV method over the competing methods.