Coupled image restoration model with non‐convex non‐smooth ℓ p wavelet frame and total variation regularisation

Abstract

In this study, the authors propose a coupled analysis-based image restoration model regularised by total variation(TV) and wavelet frame coefficients penalty terms imposed on non-convex non-smooth lp-norm (0<p<1). The highlighted contributions to this model are: (i) the intrinsic quality of preserving piecewise smooth areas of TV and the amazing sparse representing capability of the wavelet frame to the underlying image alternately interact, will lead to better experimental results; and (ii) the non-convex non-smooth lp-norm (0<p<1) regularisation is more amenable to the marginal distributions of gradients of natural images than l1-norm, which will suppress staircase effects more effectively. By alternative direction method of multipliers, the objective function is first divided into three subproblems that are solved by the fast iterative shrinkage-thresholding algorithm (FISTA) and the generalised iterated shrinkage algorithm (GISA) respectively. The GISA solution is computationally more efficient than a diversity of algorithms such as iteratively reweighted L1( IRL1), iteratively reweighted least squares (IRLS) restricted to solve non-convex non-decreasing function; and the FISTA solution also has a faster convergence rate than iterative shrinkage-thresholding algorithm. The extensive experimental results show that the proposed model exhibit an amazing image restoration capability.