Image Restoration Using Joint Statistical Modeling in Space-Transform Domain

This paper presents a novel strategy for high-fidelity image restoration by characterizing both local smoothness and nonlocal self-similarity of natural images in a unified statistical manner. The main contributions are three-folds. First, from the perspective of image statistics, a joint statistical modeling (JSM) in an adaptive hybrid space-transform domain is established, which offers a powerful mechanism of combining local smoothness and nonlocal self-similarity simultaneously to ensure a more reliable and robust estimation. Second, a new form of minimization functional for solving image inverse problem is formulated using JSM under regularization-based framework. Finally, in order to make JSM tractable and robust, a new Split-Bregman based algorithm is developed to efficiently solve the above severely underdetermined inverse problem associated with theoretical proof of convergence. Extensive experiments on image inpainting, image deblurring and mixed Gaussian plus salt-and-pepper noise removal applications verify the effectiveness of the proposed algorithm.Comment: 14 pages, 18 figures, 7 Tables, to be published in IEEE Transactions on Circuits System and Video Technology (TCSVT). High resolution pdf version and Code can be found at: http://idm.pku.edu.cn/staff/zhangjian/IRJSM

Recent Progress in Image Deblurring

This paper comprehensively reviews the recent development of image deblurring, including non-blind/blind, spatially invariant/variant deblurring techniques. Indeed, these techniques share the same objective of inferring a latent sharp image from one or several corresponding blurry images, while the blind deblurring techniques are also required to derive an accurate blur kernel. Considering the critical role of image restoration in modern imaging systems to provide high-quality images under complex environments such as motion, undesirable lighting conditions, and imperfect system components, image deblurring has attracted growing attention in recent years. From the viewpoint of how to handle the ill-posedness which is a crucial issue in deblurring tasks, existing methods can be grouped into five categories: Bayesian inference framework, variational methods, sparse representation-based methods, homography-based modeling, and region-based methods. In spite of achieving a certain level of development, image deblurring, especially the blind case, is limited in its success by complex application conditions which make the blur kernel hard to obtain and be spatially variant. We provide a holistic understanding and deep insight into image deblurring in this review. An analysis of the empirical evidence for representative methods, practical issues, as well as a discussion of promising future directions are also presented.Comment: 53 pages, 17 figure

Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity

A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the proposed framework with structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared to traditional sparse inverse problem techniques. This interpretation also suggests an effective dictionary motivated initialization for the MAP-EM algorithm. We demonstrate that in a number of image inverse problems, including inpainting, zooming, and deblurring, the same algorithm produces either equal, often significantly better, or very small margin worse results than the best published ones, at a lower computational cost.Comment: 30 page

Line-Field Based Adaptive Image Model for Blind Deblurring

Ph.DDOCTOR OF PHILOSOPH

Dictionary Learning for Deblurring and Digital Zoom

This paper proposes a novel approach to image deblurring and digital zooming using sparse local models of image appearance. These models, where small image patches are represented as linear combinations of a few elements drawn from some large set (dictionary) of candidates, have proven well adapted to several image restoration tasks. A key to their success has been to learn dictionaries adapted to the reconstruction of small image patches. In contrast, recent works have proposed instead to learn dictionaries which are not only adapted to data reconstruction, but also tuned for a specific task. We introduce here such an approach to deblurring and digital zoom, using pairs of blurry/sharp (or low-/high-resolution) images for training, as well as an effective stochastic gradient algorithm for solving the corresponding optimization task. Although this learning problem is not convex, once the dictionaries have been learned, the sharp/high-resolution image can be recovered via convex optimization at test time. Experiments with synthetic and real data demonstrate the effectiveness of the proposed approach, leading to state-of-the-art performance for non-blind image deblurring and digital zoom

A new bandwidth adaptive non-local kernel regression algorithm for image/video restoration and its GPU realization

This paper presents a new bandwidth adaptive nonlocal kernel regression (BA-NLKR) algorithm for image and video restoration. NLKR is a recent approach for improving the performance of conventional steering kernel regression (SKR) and local polynomial regression (LPR) in image/video processing. Its bandwidth, which controls the amount of smoothing, however is chosen empirically. The proposed algorithm incorporates the intersecting confidence intervals (ICI) bandwidth selection method into the framework of NLKR to facilitate automatic bandwidth selection so as to achieve better performance. A parallel implementation of the proposed algorithm is also introduced to reduce significantly its computation time. The effectiveness of the proposed algorithm is illustrated by experimental results on both single image and videos super resolution and denoising.published_or_final_versio