  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.
