Adaptive regularization parameter for nonconvex TGV based image restoration.

• This article proposes a novel nonconvex TGV model for adaptive image restoration. • We develop in detail a highly efficient alternating direction method of multipliers. • The regularization parameter λ can be automatically estimated during the iteration. • Based on convex analysis, a novel convergence proof of our algorithm is presented. • Our scheme provide promising performance in restoration accuracy and visual quality. Overcoming the staircase effect and simultaneously preserving edge details is an important and challenging issue in image processing. To this aim, this paper investigates the nonconvex total generalized variation regularization model for image restoration. Numerically, a highly efficient alternating direction method of multipliers is constructed to deal with the optimization problem in detail, which closely incorporates the superiorities of iteratively reweighted ℓ 1 algorithm and variable splitting technique. The proposed strategy can efficiently achieve image restoration and adaptive parameter estimation by applying Morozov's discrepancy principle. Furthermore, the convergence property of our novel algorithm with the variable regularization parameter is presented. Finally, numerical simulations concertedly illustrate that our approach outperforms several state-of-the-art regularization models, in terms of reconstruction accuracy and edge-preserving ability. [ABSTRACT FROM AUTHOR]