A study on CT sinogram statistical distribution by information divergence theory

In low-dose X-ray computed tomography (CT) image reconstruction, accurate modeling of the statistical properties of the measured data (i.e., both the transmission data and the sinogram data after linearity calibration) is essential to achieve high diagnostic image quality. By current X-ray CT systems, the acquired transmission data can be described by a compound Poisson distribution upon an electronic noise background. Such a statistical distribution is numerically intractable for image reconstruction. On the other hand, the sinogram data can be easily manipulated for image reconstruction, but lack a statistical description for optimal reconstruction in low-dose applications. In this paper, we propose the use of information divergence theory to describe the statistical distribution of the sinogram data. Specifically, the αdivergence, as a typical example, is adapted to fit the low-dose CT sinogram data. To minimize the associated cost function for frequency curve fitting, the exponential functional family was chosen and the Minka's fixed-point numerical calculation scheme was employed. By repeatedly scans from an anthropomorphic torso phantom at several mAs levels from normal- to low-dose imaging, the corresponding α values were fitted. As the mAs level increased toward normaldose imaging, the corresponding α value approached to favor a normal distribution, as expected. As the mAs level decreased toward low-dose imaging, the corresponding a value approached to deviate away from a normal distribution. These experimental observations indicated that the α-divergence measure can describe the statistical distributions of the sinogram data and, therefore, has the potential to be a cost function for statistical reconstruction of low-dose CT images.