CT reconstruction method from truncated projection based on FSM analytic continuation

Abstract

The importance of performing exact image reconstruction from the minimum amount of data has been recognized for a longtime. Yangbo Ye et al. has proved that the interior problem can be exactly and stably solved if a subregion in an ROI/VOI in the FOV is known from fan-beam/cone-beam projection datasets using the analytic continuation technique. But the analytic continuation is a very ill-posed question. Conventional methods are iterative or not suited to multi-region-known situation. In this work we proposed a novel method based on fundamental solution method (FSM) analytic continuation to reconstruct whole object from truncated projection with a known subregion. First we translate the analytic continuation problem to an equivalent Cauchy problems of Laplace equation. And then we use the FSM method to solve the problem numrically. Because the problem is very ill-posed, we adopt Tikhonov regularization in chord reconstruction. And we can use Singular Value Decomposition (SVD) to accelerate the algorithm. The method is a fast analytical algorithm and can be applied to multi-region-known situation.