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A Second Order Nonsmooth Variational Model for Restoring Manifold-Valued Images
TLDR
We introduce a new nonsmooth variational model for the restoration of manifold-valued data which includes second order differences in the regularization term, which up to now only existed for cyclic data. Expand
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Second Order Differences of Cyclic Data and Applications in Variational Denoising
TLDR
In many image and signal processing applications, such as interferometric synthetic aperture radar (SAR), electroencephalogram (EEG) data analysis, ground-based astronomy, and color image restoration, in HSV or LCh spaces the data has its range on the one-dimensional sphere $\mathbb S^1$. Expand
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Restoration of Manifold-Valued Images by Half-Quadratic Minimization
The paper addresses the generalization of the half-quadratic minimization method for the restoration of images having values in a complete Riemannian manifold. We recall the half-quadraticExpand
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A Second-Order TV-Type Approach for Inpainting and Denoising Higher Dimensional Combined Cyclic and Vector Space Data
  • R. Bergmann, A. Weinmann
  • Computer Science, Mathematics
  • Journal of Mathematical Imaging and Vision
  • 12 January 2015
TLDR
We develop algorithms for the solution of the corresponding second-order total variation-type problems for denoising, inpainting as well as the combination of both. Expand
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A Parallel Douglas-Rachford Algorithm for Minimizing ROF-like Functionals on Images with Values in Symmetric Hadamard Manifolds
TLDR
We are interested in restoring images having values in a symmetric Hadamard manifold by minimizing a functional with a quadratic data term and a total variation--like regularizing term. To solve the convex minimization problem, we extend the Douglas--Rachford algorithm and its parallel version to symmetric manifolds. Expand
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Priors with Coupled First and Second Order Differences for Manifold-Valued Image Processing
TLDR
We generalize discrete variational models involving the infimal convolution (IC) of first and second order differences and the total generalized variation (TGV) to manifold-valued images. Expand
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A Graph Framework for Manifold-Valued Data
TLDR
Graph-based methods have been proposed as a unified framework for discrete calculus of local and nonlocal image processing methods in recent years. Expand
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Nonlocal Inpainting of Manifold-Valued Data on Finite Weighted Graphs
TLDR
We introduce a new graph infinity-Laplace operator based on the idea of discrete minimizing Lipschitz extensions, which we use to formulate the inpainting problem as PDE on the graph. Expand
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Fenchel Duality Theory and A Primal-Dual Algorithm on Riemannian Manifolds
TLDR
This paper introduces a new notion of a Fenchel conjugate to functions defined on Riemannian manifolds. Expand
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Iterative Multiplicative Filters for Data Labeling
TLDR
We propose a new iterative multiplicative filtering algorithm for label assignment matrices which can be used for the supervised partitioning of manifold-valued images. Expand
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