Image Restoration Via Sparse Optimization

Images are an essential medium for recording and sharing visual information,which plays a significant role in analyzing and exploring the knowledge in human society.With the development of manufacturing industry and imaging techIologies,more diversified and u biquitous devices are used for imaging.However,limited by the hardware of image device and imaging timing,images are often distorted by various degeneration factors,e.g.noise,blur,and saturation.In the real applications,it is expensive to upgrade the imaging devica and impractical to retaking the photos or videos.To boost the image-based information recording and analysis,we resort to restoxing high-quality images from the degenerated images:Therefore,as a fundamental tool,image restoration a crucial task for all image-based applications.In this dissertation,we focus on low-quality degenerated image restoration.The works ii this dissertation were supported by the Key Program of National Natural Sci-ence Foundation.The core task and key of the image restoration are building proper and representative image models as well as effective and robust optimitation methods.Con-sidering that the high dimensional images usually distributes on a latent low-dimensional sparse space,sparsity is thus a powerful tool for modeling the data.In this thesis,we thus focus on the sparsity-based image models,correspornding sparse Dptimization technologies as well as the applications on image restoration problems.The main contributions of this thesis are summarized as follows;1.This thesis proposes a matching pursuit based total variation algorithm(MPTV) for image restoration.Total variation(TV)regularization encourages the sparsity on image gradients to preserve sharp image edges during image restoration.This thesis proposes a new TV-based model by introducing a binary indicator to identify the nonzero elements in the sparse image gradients,A corresponding matching pursuit based total variation minimization method(MPTV)is proposed based on the cutting-plane algorithm.MPTV suffers from less regularization bias and performs more robust,which outperforms the previous methods on many image restorations.2.This thesis proposes a blind image restoration method based on automatic gradient activation.This thesis conducts a theoretical analysis of the non-convex and ill-posed blind image restoration problem and shows that a subset of the gradients is adequate to estimate the blur kernel robu.stly.Based on above theory,this thesis further introduces a gradient activation method to automatically select a subset of gradients of the latent image in a cutting-plane-based optimization scheme for image restoration.No extra assumption is used in out model,which greatly improves the accuracy and flexibility.Experiments demonstrate the effectiveness and robustness of the proposed method in comparison with the state-of-the-art methods.3.This thesis proposes a self-paced estimation based robust image restoration method.Rather than attempt to identify outliers to the model a priori,the proposed method instead sequentially identify inliers,and gradually incorporate them into the estima?tion process.The self-paced estimation scheme gradually detects the and includes reliable inlier pixel sets into the updating process.Experiments show the effective-ness and robustness of the proposed method compared to previous state-of-the-art methods.4.This thesis proposes to learn an optimizer for image restoration task.The predomi-nant approach is based on optimization subject to regularization functions.Existing learning based methods solely focus on learning a prior.We address the gap between the optimization-based and learning-based approaches by learning an optimizer.We propose a Recurrent Gradient Descent Network(RGDN)by systematically incor-porating deep neural networks into a fully parameterized gradient descent scheme.By training on various examples,the RGDN learns an implicit image prior and a universal parameter free update rule through recnrsive supervision.Extensive ex-periments demonstrate that the proposed method is effective and robust to produce favorable results well practical for real-world applications.