Flow smoothing and denoising: graph signal processing in the edge-space
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...
| Main Authors: | , |
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| Format: | Conference item |
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IEEE
2019
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| _version_ | 1797097044977909760 |
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| author | Schaub, M Segarra, S |
| author_facet | Schaub, M Segarra, S |
| author_sort | Schaub, M |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T04:50:04Z |
| format | Conference item |
| id | oxford-uuid:d4a55c96-8ddd-4850-919a-25f351f0240e |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:50:04Z |
| publishDate | 2019 |
| publisher | IEEE |
| record_format | dspace |
| spelling | oxford-uuid:d4a55c96-8ddd-4850-919a-25f351f0240e2022-03-27T08:20:07ZFlow smoothing and denoising: graph signal processing in the edge-spaceConference itemhttp://purl.org/coar/resource_type/c_5794uuid:d4a55c96-8ddd-4850-919a-25f351f0240eSymplectic Elements at OxfordIEEE2019Schaub, MSegarra, SThis 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. |
| spellingShingle | Schaub, M Segarra, S Flow smoothing and denoising: graph signal processing in the edge-space |
| title | Flow smoothing and denoising: graph signal processing in the edge-space |
| title_full | Flow smoothing and denoising: graph signal processing in the edge-space |
| title_fullStr | Flow smoothing and denoising: graph signal processing in the edge-space |
| title_full_unstemmed | Flow smoothing and denoising: graph signal processing in the edge-space |
| title_short | Flow smoothing and denoising: graph signal processing in the edge-space |
| title_sort | flow smoothing and denoising graph signal processing in the edge space |
| work_keys_str_mv | AT schaubm flowsmoothinganddenoisinggraphsignalprocessingintheedgespace AT segarras flowsmoothinganddenoisinggraphsignalprocessingintheedgespace |