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,the penalized weighted least-square(PWLS)smoothing framework is a choice for an optimal solution.It utilizes the prior variance -mean relationship to construct 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-correla tion,the K-L transform maximizes the data variance represented by each component and simplifies the task of3D filtering into2D 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 and3D 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 reduction without the loss of resolution.