Half Quadratic Regularization Model for Image Restoration

Image restoration easily smears image edge in unsteady area and produces stair effect in steady area. In order to overcome these shortcomings, the paper proposes a half-quadratic energy functional regularization model (EFRM) and structured Newton iterative algorithm. Firstly, for blurred image by system and Gaussian noise, fitting term is described by L-2 norm, regularization term is described by half-quadratic function, which can accurately describe image singular property, and the fitting term and regularization term constitute image restoration EFRM. Secondly, resort to Fenchel transform, by introducing auxiliary variables, the primal EFRM is converted into augmented image restoration EFRM. Finally, take advantage of preconditioned theory, Hessian matrix of the transformed model is structured, a new Newton project iterative algorithm is proposed. Comparing to several state-of-art approaches, numerical experiment results show that the proposed EFRM can effectively protect image edge and reduce stair effect, and show better visual effect and higher peak signal-to-noise ratio (PSNR).