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author:

Chen, Fei (Chen, Fei.) [1] (Scholars:陈飞) | Cheung, Gene (Cheung, Gene.) [2] | Zhang, Xue (Zhang, Xue.) [3]

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Abstract:

In the graph signal processing (GSP) literature, it has been shown that signal-dependent graph Laplacian regularizer (GLR) can efficiently promote piecewise constant (PWC) signal reconstruction for various image restoration tasks. However, for planar image patches, like total variation (TV), GLR may suffer from the well-known 'staircase' effect. To remedy this problem, we generalize GLR to gradient graph Laplacian regularizer (GGLR) that provably promotes piecewise planar (PWP) signal reconstruction for the image interpolation problem—a 2D grid with random missing pixels that requires completion. Specifically, we first construct two higher-order gradient graphs to connect local horizontal and vertical gradients. Each local gradient is estimated using structure tensor, which is robust using known pixels in a small neighborhood, mitigating the problem of larger noise variance when computing gradient of gradients. Moreover, unlike total generalized variation (TGV), GGLR retains the quadratic form of GLR, leading to an unconstrained quadratic programming (QP) problem per iteration that can be solved quickly using conjugate gradient (CG). We derive the means-square-error minimizing weight parameter for GGLR, trading off bias and variance of the signal estimate. Experiments show that GGLR outperformed competing schemes in interpolation quality for severely damaged images at a reduced complexity. © 2021 IEEE

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  • [ 1 ] [Chen, Fei]College of Mathematics and Computer Science, Fuzhou University, Fuzhou, China
  • [ 2 ] [Cheung, Gene]Dept of EECS, York University, Toronto, Canada
  • [ 3 ] [Zhang, Xue]Dept of EECS, York University, Toronto, Canada

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ISSN: 1522-4880

Year: 2021

Volume: 2021-September

Page: 1964-1968

Language: English

Cited Count:

WoS CC Cited Count:

SCOPUS Cited Count: 10

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 2

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