Study On Image Restoration Via L₀ Regularization

In the last few decades,image and video have become the main carriers of visual signals for digital multimedia content along with the rapid development of information technology.In addition,the quality of digtal images also plays an improtant role in the process of visual perception and communication.Since the degradations of digital images are inevitable in real life,the image restoration technology has been a hot subject in the field of image processing.It now has evolved into an energetic field at the intersection of image processing,computer vision and computational imaging.Since digital images are usually sparse in the wavelet frame domain,some nonconvex minimization models based on wavelet frame have been proposed and sparse approximations have been widely used in image restoration in recent years.In this paper,we consider a nonconvex image restoration model which the objective functional of the proposed model uses the l₀ norm to measure the sparsity of the resulting image in a tight framelet system.The proximal alternating iterative hard thresholding method is proposed to solve the above model.Through combining the proposed algorithm with the iterative hard threshoding algorithm which is well studied in compressed sensing theory,this paper proves that the complexity of the proposed method is ????1/????.On the other hand,the special form of the above nonconvex minimization mode also motivates us to study a more general nonconvex and nonsmooth problems of the form:minimize,where f is a convex function,g is nonconvex function and the function H is strongly convex.We thus introduce the pseudo proximal alternating linearized minimization method for solving the above problems.Building on the powerful Kurdyka-Lojasiewicz property,we derive a convergence analysis and establish that each bounded sequence generated by the proposed algorithm globally converges to a critical point of the corresponding model.Finally,the proposed method is applied to restore the blurred noisy gray images.As the numerical results reveal,the performance of the proposed method is comparable or better than some well-known convex image restoration methods.