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Neural Computing and Applications
Erschienen in: Neural Computing and Applications 11/2018

26.10.2016 | Original Article

Learning sparse partial differential equations for vector-valued images

verfasst von: Yuanyuan Jiao, Xiaogang Pan, Zhenyu Zhao, Chenping Hou

Erschienen in: Neural Computing and Applications | Ausgabe 11/2018

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Abstract

Learning partial differential equations (LPDEs) from training data for particular tasks has been successfully applied to many image processing problems. In this paper, we propose a more effective LPDEs model for vector-valued image tasks. The PDEs are also formulated as a linear combination of fundamental differential invariants, but have several distinctions. First, we simplify the current LPDEs system by omitting a PDE which works as an indicate function in current ones. Second, instead of using \(L_2\)-norm, we use the \(L_1\)-norm to regularize the coefficients with respect to the fundamental differential invariants. Third, as the objective function is not smooth, we resort to the alternating direction method to optimize it. We illustrate the properties of our LPDEs system by several examples in denoising and demosaicking of RGB color images. The experiments demonstrate the advantage of the proposed method over other PDE-based methods.
Vorheriger Artikel A new approach to fuzzy group decision making with trapezoidal fuzzy preference relations by using compatibility measure
Nächster Artikel Neural network-based discrete-time Z-type model of high accuracy in noisy environments for solving dynamic system of linear equations

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Fußnoten
1
The images are padded with zeros of several pixels width around them, so that the Dirichlet boundary conditions \(u_{m}(x,y,t)=0, v_{m}(x,y,t)=0, (x,y,t)\in \varGamma\), are naturally fulfilled.
 
2
The images are padded with zeros of several pixels width around them such that the Dirichlet boundary conditions \(u^c_{m}(x,y,t)=0, (x,y,t)\in \varGamma\), are naturally fulfilled.
 
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Metadaten
Titel
Learning sparse partial differential equations for vector-valued images
verfasst von
Yuanyuan Jiao
Xiaogang Pan
Zhenyu Zhao
Chenping Hou
Publikationsdatum
26.10.2016
Verlag
Springer London
Erschienen in
Neural Computing and Applications / Ausgabe 11/2018
Print ISSN: 0941-0643
Elektronische ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-016-2623-y

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