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

Video modeling via implicit motion representations

Video modeling refers to the development of analytical representations for explaining the intensity distribution in video signals. Based on the analytical representation, we can develop algorithms for accomplishing particular video-related tasks. Therefore video modeling provides us a foundation to bridge video data and related-tasks. Although there are many video models proposed in the past decades, the rise of new applications calls for more efficient and accurate video modeling approaches.;Most existing video modeling approaches are based on explicit motion representations, where motion information is explicitly expressed by correspondence-based representations (i.e., motion velocity or displacement). Although it is conceptually simple, the limitations of those representations and the suboptimum of motion estimation techniques can degrade such video modeling approaches, especially for handling complex motion or non-ideal observation video data. In this thesis, we propose to investigate video modeling without explicit motion representation. Motion information is implicitly embedded into the spatio-temporal dependency among pixels or patches instead of being explicitly described by motion vectors.;Firstly, we propose a parametric model based on a spatio-temporal adaptive localized learning (STALL). We formulate video modeling as a linear regression problem, in which motion information is embedded within the regression coefficients. The coefficients are adaptively learned within a local space-time window based on LMMSE criterion. Incorporating a spatio-temporal resampling and a Bayesian fusion scheme, we can enhance the modeling capability of STALL on more general videos. Under the framework of STALL, we can develop video processing algorithms for a variety of applications by adjusting model parameters (i.e., the size and topology of model support and training window). We apply STALL on three video processing problems. The simulation results show that motion information can be efficiently exploited by our implicit motion representation and the resampling and fusion do help to enhance the modeling capability of STALL.;Secondly, we propose a nonparametric video modeling approach, which is not dependent on explicit motion estimation. Assuming the video sequence is composed of many overlapping space-time patches, we propose to embed motion-related information into the relationships among video patches and develop a generic sparsity-based prior for typical video sequences. First, we extend block matching to more general kNN-based patch clustering, which provides an implicit and distributed representation for motion information. We propose to enforce the sparsity constraint on a higher-dimensional data array signal, which is generated by packing the patches in the similar patch set. Then we solve the inference problem by updating the kNN array and the wanted signal iteratively. Finally, we present a Bayesian fusion approach to fuse multiple-hypothesis inferences. Simulation results in video error concealment, denoising, and deartifacting are reported to demonstrate its modeling capability.;Finally, we summarize the proposed two video modeling approaches. We also point out the perspectives of implicit motion representations in applications ranging from low to high level problems

Adaptive Image Denoising by Targeted Databases

We propose a data-dependent denoising procedure to restore noisy images. Different from existing denoising algorithms which search for patches from either the noisy image or a generic database, the new algorithm finds patches from a database that contains only relevant patches. We formulate the denoising problem as an optimal filter design problem and make two contributions. First, we determine the basis function of the denoising filter by solving a group sparsity minimization problem. The optimization formulation generalizes existing denoising algorithms and offers systematic analysis of the performance. Improvement methods are proposed to enhance the patch search process. Second, we determine the spectral coefficients of the denoising filter by considering a localized Bayesian prior. The localized prior leverages the similarity of the targeted database, alleviates the intensive Bayesian computation, and links the new method to the classical linear minimum mean squared error estimation. We demonstrate applications of the proposed method in a variety of scenarios, including text images, multiview images and face images. Experimental results show the superiority of the new algorithm over existing methods.Comment: 15 pages, 13 figures, 2 tables, journa

Structure-aware image denoising, super-resolution, and enhancement methods

Denoising, super-resolution and structure enhancement are classical image processing applications. The motive behind their existence is to aid our visual analysis of raw digital images. Despite tremendous progress in these fields, certain difficult problems are still open to research. For example, denoising and super-resolution techniques which possess all the following properties, are very scarce: They must preserve critical structures like corners, should be robust to the type of noise distribution, avoid undesirable artefacts, and also be fast. The area of structure enhancement also has an unresolved issue: Very little efforts have been put into designing models that can tackle anisotropic deformations in the image acquisition process. In this thesis, we design novel methods in the form of partial differential equations, patch-based approaches and variational models to overcome the aforementioned obstacles. In most cases, our methods outperform the existing approaches in both quality and speed, despite being applicable to a broader range of practical situations.Entrauschen, Superresolution und Strukturverbesserung sind klassische Anwendungen der Bildverarbeitung. Ihre Existenz bedingt sich in dem Bestreben, die visuelle Begutachtung digitaler Bildrohdaten zu unterstützen. Trotz erheblicher Fortschritte in diesen Feldern bedürfen bestimmte schwierige Probleme noch weiterer Forschung. So sind beispielsweise Entrauschungsund Superresolutionsverfahren, welche alle der folgenden Eingenschaften besitzen, sehr selten: die Erhaltung wichtiger Strukturen wie Ecken, Robustheit bezüglich der Rauschverteilung, Vermeidung unerwünschter Artefakte und niedrige Laufzeit. Auch im Gebiet der Strukturverbesserung liegt ein ungelöstes Problem vor: Bisher wurde nur sehr wenig Forschungsaufwand in die Entwicklung von Modellen investieret, welche anisotrope Deformationen in bildgebenden Verfahren bewältigen können. In dieser Arbeit entwerfen wir neue Methoden in Form von partiellen Differentialgleichungen, patch-basierten Ansätzen und Variationsmodellen um die oben erwähnten Hindernisse zu überwinden. In den meisten Fällen übertreffen unsere Methoden nicht nur qualitativ die bisher verwendeten Ansätze, sondern lösen die gestellten Aufgaben auch schneller. Zudem decken wir mit unseren Modellen einen breiteren Bereich praktischer Fragestellungen ab