Fast gradient-based algorithm for total variation regularized tomography reconstruction

For tomography reconstruction, the iteration method based on TV (total variation) regularization is proven effective especially when projection data is insufficient or noisy due to low count levels. The purpose of this paper is to develop a fast iterative algorithm to solve this recently popular TV-regularized CT optimization problem. Using the method of surrogate function, we split the sum minimization scheme to two sub problems: minimizing weighted least square function and TV denoising with weighted norm. The conventional projection iterative methods such as ART, SART are applicable for the first sub problem. For the second one, we adopt Chambolle´s orthogonal projection scheme to avoid numerical difficulty due to the non differentiability of the TV norm. Then the solution can be obtained using the alternative iterative minimization algorithm. The proposed approach is applied to fan-beam CT with few-view data and the experiment result indicate that this approach is faster than gradient descent based TV algorithms and reconstruction image is better with same iterations. In conclusion, the proposed uncoupled algorithm is stable and efficient and it can be extended to cone-beam CT reconstruction and interior tomography easily.