Primal-dual splitting method for high-order model with application to image restoration

The total variation (TV) based iterative regularization method has been utilized to recover images degraded by blur and impulse noise. It is well-known that the TV regularization model preserves the edges well in the restored images while suffers from staircase effect. In this paper, we consider a high-order total variation minimization model which removes undesired artifacts for restoring blurry and noisy images. Then a primal-dual splitting algorithm is developed to solve the high-order minimization problem. The convergence of the proposed method is guaranteed. Numerical results illustrate that the proposed method is competitive with the state-of-the-art methods in terms of the peak signal-to-noise (PSNR) and the structural similarity index measurement (SSIM).