Modeling Mixed Poisson-Gaussian Noise in Statistical Image Reconstruction for X-Ray CT

Statistical image reconstruction (SIR) methods for X-ray CT improve the ability to produce high-quality and accurate images, while greatly reducing patient exposure to radiation. The challenge with further dose reduction to an ultralow level by lowering the X-ray tube current is photon starvation and electronic noise starts to dominate. This introduces negative or zero values into the raw data and consequently causes artifacts in the reconstructed CT images with current SIR methods based on log data. At ultra-low photon counts, the CT detector signal deviates significantly from Poisson or shifted Poisson statistics for the pre-log data and from Gaussian statistics for post-log data. This paper proposes a novel SIR method called MPG (mixed Poisson-Gaussian). It models the raw noisy measurements using a mixed Poisson-Gaussian distribution that accounts for the electronic noise. The MPG method is able to directly use the negative and zero values in the raw data without any pre-processing. We adopt the reweighted least square method to develop a tractable likelihood function that can be easily incorporated into SIR reconstruction framework. To minimize the MPG cost function containing the likelihood function and an edge-preserving regularization term, we use an Alternating Direction Method of Multipliers (ADMM) that divides the original optimization problem into several sub-problems that are easier to solve. Our results on 3D simulated cone-beam data set indicate that the proposed MPG method reduces noise in the reconstructed images comparing with the conventional FBP and statistical penalized weighted least-square (PWLS) method for ultra-low dose CT (ULDCT) imaging.