Image Restoration using Total Variation with Overlapping Group Sparsity
This addresses the problem of staircase artifacts in image restoration for imaging science, offering an incremental improvement over existing TV-based methods.
The paper tackled image restoration by proposing an overlapping group sparsity total variation regularizer to avoid staircase artifacts while preserving edges, achieving improved performance in terms of PSNR, relative error, and computing time compared to state-of-the-art methods.
Image restoration is one of the most fundamental issues in imaging science. Total variation (TV) regularization is widely used in image restoration problems for its capability to preserve edges. In the literature, however, it is also well known for producing staircase-like artifacts. Usually, the high-order total variation (HTV) regularizer is an good option except its over-smoothing property. In this work, we study a minimization problem where the objective includes an usual $l_2$ data-fidelity term and an overlapping group sparsity total variation regularizer which can avoid staircase effect and allow edges preserving in the restored image. We also proposed a fast algorithm for solving the corresponding minimization problem and compare our method with the state-of-the-art TV based methods and HTV based method. The numerical experiments illustrate the efficiency and effectiveness of the proposed method in terms of PSNR, relative error and computing time.