12-lead ECG Reconstruction via Koopman Operators

Tomer Golany*, Daniel Freedman*, Saar Minha*, Kira Radinsky*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


32% of all global deaths in the world are caused by cardiovascular diseases. Early detection, especially for patients with ischemia or cardiac arrhythmia, is crucial. To reduce the time between symptoms onset and treatment, wearable ECG sensors were developed to allow for the recording of the full 12-lead ECG signal at home. However, if even a single lead is not correctly positioned on the body that lead becomes corrupted, making automatic diagnosis on the basis of the full signal impossible. In this work, we present a methodology to reconstruct missing or noisy leads using the theory of Koopman Operators. Given a dataset consisting of full 12-lead ECGs, we learn a dynamical system describing the evolution of the 12 individual signals together in time. The Koopman theory indicates that there exists a high-dimensional embedding space in which the operator which propagates from one time instant to the next is linear. We therefore learn both the mapping to this embedding space, as well as the corresponding linear operator. Armed with this representation, we are able to impute missing leads by solving a least squares system in the embedding space, which can be achieved efficiently due to the sparse structure of the system. We perform an empirical evaluation using 12-lead ECG signals from thousands of patients, and show that we are able to reconstruct the signals in such way that enables accurate clinical diagnosis.

Original languageEnglish
Title of host publicationProceedings of the 38th International Conference on Machine Learning, ICML 2021
PublisherML Research Press
Number of pages10
ISBN (Electronic)9781713845065
StatePublished - 2021
Event38th International Conference on Machine Learning, ICML 2021 - Virtual, Online
Duration: 18 Jul 202124 Jul 2021

Publication series

NameProceedings of Machine Learning Research
ISSN (Electronic)2640-3498


Conference38th International Conference on Machine Learning, ICML 2021
CityVirtual, Online


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