Fast Regularization of Matrix-Valued Images

Rosman, Guy; Wang, Yu; Tai, Xue–Cheng; Kimmel, Ron; Bruckstein, Alfred M.

doi:10.1007/978-3-642-54774-4_2

Cited by 6 publications

(1 citation statement)

References 47 publications

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“…These can easily be introduced into real-valued state-of-the-art methods like alternating direction method of multipliers (ADMM) [37,44]. For example in [68,69] a matrix-valued TV functional was introduced using the ADMM for the classical TV functional extended by a such projection. However, when considering the example of symmetric positive definite matrices, the set is open.…”

Section: Related Workmentioning

confidence: 99%

A Graph Framework for Manifold-Valued Data

Bergmann¹,

Tenbrinck²

2018

SIAM J. Imaging Sci.

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Graph-based methods have been proposed as a unified framework for discrete calculus of local and nonlocal image processing methods in the recent years. In order to translate variational models and partial differential equations to a graph, certain operators have been investigated and successfully applied to real-world applications involving graph models. So far the graph framework has been limited to real-and vector-valued functions on Euclidean domains. In this paper we generalize this model to the case of manifold-valued data. We introduce the basic calculus needed to formulate variational models and partial differential equations for manifold-valued functions and discuss the proposed graph framework for two particular families of operators, namely, the isotropic and anisotropic graph p-Laplacian operators, p ≥ 1. Based on the choice of p we are in particular able to solve optimization problems on manifold-valued functions involving total variation (p = 1) and Tikhonov (p = 2) regularization. Finally, we present numerical results from processing both synthetic as well as real-world manifold-valued data, e.g., from diffusion tensor imaging (DTI) and light detection and ranging (LiDAR) data. * Felix-Klein-Zentrum,

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