Data-driven thresholding in denoising with Spectral Graph Wavelet Transform

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:389

Article

de Loynes, Basile¹  Navarro, Fabien²  Olivier, Baptiste³ 

[1] ENSAI, Bruz, France

[2] ENSAI, CREST, Bruz, France

[3] Orange Labs, Meylan, France

关键词: Spectral graph theory;    Denoising;    Stein unbiased risk estimation;    Spectral Graph Wavelet Transform;    Tight frame;    Variance estimation;   

DOI  :  10.1016/j.cam.2020.113319

来源: Elsevier

【 摘 要 】

This paper is devoted to adaptive signal denoising in the context of Graph Signal Processing (GSP) using Spectral Graph Wavelet Transform (SGWT). This issue is addressed via a data-driven thresholding process in the transformed domain by optimizing the parameters in the sense of the Mean Square Error (MSE) using the Stein's Unbiased Risk Estimator (SURE). The SGWT considered is built upon a partition of unity making the transform semi-orthogonal so that the optimization can be performed in the transformed domain. However, since the SGWT is over-complete, the divergence term in the SURE needs to be computed in the context of correlated noise. Two thresholding strategies called coordinatewise and block thresholding process are investigated. For each of them, the SURE is derived for a whole family of elementary thresholding functions among which the soft threshold and the James-Stein threshold. This multi-scales analysis shows better performance than the most recent methods from the literature. That is illustrated numerically for a series of signals on different graphs. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free