Analytic noise propagation for anisotropic denoising of CT images

In X-ray Computed Tomography (CT) the measured projections and consequently the reconstructed CT images are subject to quantum and electronics noise. While noise in the projections can be well described and estimated with a corresponding physics model, the distribution of noise in the reconstructed CT images is not directly evident. Due to attenuation variations along different directions, the nature of noise in CT images is non-stationary and directed. This complicates the direct application of standard post-processing methods like bilateral filtering. In this article we describe a possibility to compute precise orientation dependent noise estimates for every pixel position. This is done by analytic propagation of projection noise estimates through indirect fan-beam filtered backprojection reconstruction. The resulting orientation dependent image noise estimates are subsequently used in adaptive bilateral filters. Taking into account the non-stationary and non-isotropic nature of noise in CT images, an average improvement in SNR of about 60% is achieved compared to linear filtering at the same resolution.