Hybrid Pre-Log and Post-Log Image Reconstruction for Computed Tomography

Tomographic image reconstruction for low-dose computed tomography (CT) is increasingly challenging as dose continues to reduce in clinical applications. Pre-log domain methods and post-log domain methods have been proposed individually and each method has its own disadvantage. While having the potential to improve image quality for low-dose data by using an accurate imaging model, pre-log domain methods suffer slow convergence in practice due to the nonlinear transformation from the image to measurements. In contrast, post-log domain methods have fast convergence speed but the resulting image quality is suboptimal for low dose CT data because the log transformation is extremely unreliable for low-count measurements and undefined for negative values. This paper proposes a hybrid method that integrates the pre-log model and post-log model together to overcome the disadvantages of individual pre-log and post-log methods. We divide a set of CT data into high-count and low-count regions. The post-log weighted least squares model is used for measurements in the high-count region and the pre-log shifted Poisson model for measurements in the low-count region. The hybrid likelihood function can be optimized using an existing iterative algorithm. Computer simulations and phantom experiments show that the proposed hybrid method can achieve faster early convergence than the pre-log shifted Poisson likelihood method and better signal-to-noise performance than the post-log weighted least squares method.