Noise Reduction by Projection Direction Dependent Diffusion for Low Dose Fan-beam X-ray Computed Tomography

We propose a novel method to reduce the noise in fan-beam computed tomography (CT) imaging. First, the inverse Radon transform is induced for a family of differential expression of projection function. Second, the diffusion partial differential equation (PDE) is generalized from image space to projection space in parallel-beam geometry. Third, the diffusion PDE is further induced from parallel-beam geometry to fan-beam geometry. Finally, the projection direction dependent diffusion is developed to reduce CT noise, which arises from the quantum variation in the low dose exposure of a medical x-ray CT (XCT) system. The proposed noise reduction processes projections iteratively and dependently on x-ray path position, followed by a general CT reconstruction. Numerical simulation studies have demonstrated its feasibility in the noise reduction of low dose fan-beam XCT imaging.