Analytical noise treatment for low-dose CT projection data by penalized weighted least-square smoothing in the K-L domain

By analyzing the noise properties of calibrated low-dose Computed Tomography (CT) projection data, it is clearly seen that the data can be regarded as approximately Gaussian distributed with a nonlinear signal-dependent variance. Based on this observation, a penalized weighted least-square (PWLS) smoothing framework is a choice for an optimal solution. It utilizes the prior variance-mean relationship to construct both the weight matrix and the two-dimensional (2D) spatial information as the penalty or regularization operator. Furthermore, a K-L transform is applied along the z (slice) axis to further consider the correlation among different sinograms, resulting in a PWLS smoothing in the K-L domain. As a tool for feature extraction and de-correlation, the K-L transform maximizes the data variance represented by each component and simplifies the task of 3D filtering into 2D spatial process slice by slice. Therefore, by selecting an appropriate number of neighboring slices, the K-L domain PWLS smoothing fully utilizes the prior statistical knowledge and 3D spatial information for an accurate restoration of the noisy low-dose CT projections in an analytical manner. Experimental results demonstrate that the proposed method with appropriate control parameters improves the noise treatment without sacrifice of resolution.