Douglas-rachford algorithm and tv regularization for X-rays image reconstruction

In this paper, an effective method for minimizing a convex criterion is proposed to allow its application in solving inverse problems related to the X-ray tomography. Proximal algorithms associated to total variation regularization are used knowing that they have high quality to converge. The main objective is to obtain high quality reconstructed images. We applied this algorithm to non-destructive evaluation of material in the case of 2D reconstruction of X-rays tomographic images containing real defects. The obtained results are promising and demonstrate the benefits of the proposed approach.