Augmented Total Variation Regularization in Radon-Type Inverse Problems

We introduce the augmented total variation ($TV$) regularization method for Radon-type inverse problems. Our novel approach incorporates a dual variable into the regularization process, thereby extending and essentially augmenting traditional $TV$ regularization techniques. The proposed method is robust, requiring only one algorithmic iteration to achieve accurate reconstructions. Numerical experiments on a modified Shepp–Logan phantom demonstrate that the augmented $TV$ regularization consistently yields higher structural similarity index metric (SSIM) values and lower mean absolute difference (MAD) values compared to filtered backprojection and standard $TV$ regularization. These findings indicate that our method not only reduces reconstruction errors but also preserves structural details.