Flow smoothing and denoising: graph signal processing in the edge-space

Conference item

This paper focuses on devising graph signal processing tools for the treatment of data defined on the edges of a graph. We first show that conventional tools from graph signal processing may not be suitable for the analysis of such signals. More specifically, we discuss how the underlying notion of a ‘smooth signal’ inherited from (the typically considered variants of) the graph Laplacian are not suitable when dealing with edge signals that encode a notion of flow. To overcome this limitation we introduce a class of filters based on the Edge-Laplacian, a special case of the Hodge-Laplacian for simplicial complexes of order one. We demonstrate how this Edge-Laplacian leads to low-pass filters that enforce (approximate) flow-conservation in the processed signals. Moreover, we show how these new filters can be combined with more classical Laplacian-based processing methods on the line-graph. Finally, we illustrate the developed tools by denoising synthetic traffic flows on the London street network.

Authors: Schaub, M; Segarra, S

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: IEEE
• Host title: 2018 IEEE Global Conference on Signal and Information Processing (GlobalSIP)
• Journal: 6th IEEE Global Conference on Signal and Information Processing
• Pages: 735-739
• Publication date: 2019-02-21
• Acceptance date: 2018-09-07
• DOI: 10.1109/GlobalSIP.2018.8646701
• ISBN: 9781728112954
• Keywords: Hodge-Laplacian; graph signal processing; simplicial complexes; flow denoising