Abstract
Reconstructing simplicial signals, e.g., signals defined on nodes, edges, triangles, etc., of a network, from (partial) noisy observation is of interest in water/traffic flow estimation or currency exchange markets. Typically, this concerns solving a regularised problem w.r.t. the l2 norm of the divergence or the curl of the signal, i.e., the netflows at nodes and in triangles. Realworld simplicial signals are intrinsically divergence- or curl-free, which makes l2 regularizers inapplicable. To overcome this, we develop a simplicial trend filter (STF) by regularising the total divergence and the curl via their l1 norm. By tuning two scalars, the STF can reduce independently the divergence and curl much more than smooth filtering, leading to a better reconstructed signal. The SFT is a convex problem and can be solved by fast iterative algorithms. We apply the SFT to interpolation and denoising tasks in forex and music/artist transition recordings and show its superior performance to alternatives.
Original language | English |
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Title of host publication | Proceedings of the 56th Asilomar Conference on Signals, Systems and Computers |
Editors | Michael B. Matthews |
Publisher | IEEE |
Pages | 930-934 |
Number of pages | 5 |
ISBN (Electronic) | 978-1-6654-5906-8 |
ISBN (Print) | 978-1-6654-5907-5 |
DOIs | |
Publication status | Published - 2022 |
Event | 56th Asilomar Conference on Signals, Systems and Computers, ACSSC 2022 - Virtual, Online, United States Duration: 31 Oct 2022 → 2 Nov 2022 |
Publication series
Name | Conference Record - Asilomar Conference on Signals, Systems and Computers |
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Volume | 2022-October |
ISSN (Print) | 1058-6393 |
Conference
Conference | 56th Asilomar Conference on Signals, Systems and Computers, ACSSC 2022 |
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Country/Territory | United States |
City | Virtual, Online |
Period | 31/10/22 → 2/11/22 |
Bibliographical note
Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-careOtherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.
Funding Information:
Emails: m.yang-2, [email protected]. This work is supported by the TU Delft AI Labs Programme.