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

Second-order Shape Optimization for Geometric Inverse Problems in Vision

We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian, which is generally hard to compute and suffers from a series of degeneracies. Our analysis highlights the role of mean curvature motion in comparison with first-order schemes: instead of surface area, our approach penalizes deformation, either by its Dirichlet energy or total variation. Latter regularizer sparks the development of an alternating direction method of multipliers on triangular meshes. Therein, a conjugate-gradients solver enables us to bypass formation of the Gaussian normal equations appearing in the course of the overall optimization. We combine all of the aforementioned ideas in a versatile geometric variation-regularized Levenberg-Marquardt-type method applicable to a variety of shape functionals, depending on intrinsic properties of the surface such as normal field and curvature as well as its embedding into space. Promising experimental results are reported