Augmented Total Variation Regularization in Radon‐Type Inverse Problems

ABSTRACT We introduce the augmented total variation () regularization method for Radon‐type inverse problems. Our novel approach incorporates a dual variable into the regularization process, thereby extending and essentially augmenting traditional 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 regularization consistently yields higher structural similarity index metric (SSIM) values and lower mean absolute difference (MAD) values compared to filtered backprojection and standard regularization. These findings indicate that our method not only reduces reconstruction errors but also preserves structural details.