Noise reduction for low-dose x-ray computed tomography

Low-dose X-ray computed tomography (CT) is clinically desired. This research aims to reduce the X-ray radiation delivered to patients during CT procedures by lowering the X-ray tube current or scanning time (mAs) and by developing a software approach to reduce noise associated with low-dose scans. The noise in low-dose CT was treated in two steps: (1) image reconstruction and (2) sinogram restoration. An area-weighting filtered backprojection (FBP) algorithm was proposed for fan-beam CT reconstruction. It was shown that this spatially variant area-weighting FBP algorithm could suppress the noise and solve the non-uniform noise propagation problem that otherwise occurs in the linear interpolation FBP algorithm. The noise properties of the CT sinogram (after calibration and logarithm transform) were studied by using repeated measurements. The noise of the CT sinogram was found to approximately follow the Gaussian distribution and the mean variance relationship of the CT projection data can be described by an analytical formula. Based on the noise properties of the CT sinogram, a penalized weighted least-square (PWLS) criterion was proposed to restore the CT sinogram, where a Markov random field (MRF) model was chosen as the roughness penalty. The Karhunen-Loeve (KL) transform was proposed to account for the correlation among the neighboring views in a 2D CT sinogram. By using the KL transform, an analytical solution was available for minimization of the PWLS objective function. Based on the same noise model, a fully iterative PWLS image reconstruction method was also studied. Comparison studies show that the strategy of the KL domain PWLS sinogram restoration plus area weighting FBP can achieve the same image quality as the iterative image reconstruction with much higher computation efficiency. Quantitative analysis, using noise resolution trade-off curve and receiver of characteristic (ROC), shows comparable performance between the proposed strategy and the fully iterative statistical image reconstruction method. The proposed KL domain PWLS algorithm was also developed for noise reduction of 3D Helical CT.