Total Variation Regularization Approach for Abel Transform Based Image Reconstruction

摘要

We consider Abel transform based density reconstruction for axially symmetric objects from a single radiograph by fan-beam x-rays. All contemporary methods assume that the density is piecewise constant or linear. This is quite a restrictive approximation. Our proposed model is based on high-order total variation regularization. Its main advantage is to reduce the staircase effect and enable the recovery of smoothly varying regions. We compare our model with other potential regularization techniques, like TV (Total Variation), TGV (Total Generalized Variation), LLT (Lysaker, Lundervold and Tai). The numerical tests show that the proposed model has advantages on staircasing reduction, density level preservation, CPU time and SNR (Signal Noise Ratio) value improvement.