Fast Hessian Frobenius Norm Based Image Restoration

A projected gradient algorithm (PGA) which is derived from the majorization-minimization (MM) framework has been proposed recently for Hessian-matrix Frobenius norm regularization image restoration model so that it currently provides state-of-the-art performance. Outside the MM framework and for the sake of further accelerating the convergence speed, this paper presents an efficient algorithm for image restoration under the Hessian-matrix Frobenius norm regularization. Using variable splitting to obtain an equivalent constrained optimization formulation, then our algorithm is addressed with an augmented Lagrangian method. Under the alternating direction method of multipliers (ADMM) framework, a fast algorithm with split augmented Lagrangian shrinkage scheme is thus proposed for image restoration. Finally, experimental results demonstrate that our algorithm achieves better results than PGA in terms of peak signal to noise ratio (PSNR) and convergence rate.