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dc.contributor.authorBabadi, Behtash
dc.contributor.authorPurdon, Patrick L.
dc.contributor.authorBrown, Emery N.
dc.contributor.authorBa, Demba E.
dc.date.accessioned2015-06-15T16:48:18Z
dc.date.available2015-06-15T16:48:18Z
dc.date.issued2014-12
dc.date.submitted2013-11
dc.identifier.issn0027-8424
dc.identifier.issn1091-6490
dc.identifier.urihttp://hdl.handle.net/1721.1/97419
dc.description.abstractClassical nonparametric spectral analysis uses sliding windows to capture the dynamic nature of most real-world time series. This universally accepted approach fails to exploit the temporal continuity in the data and is not well-suited for signals with highly structured time–frequency representations. For a time series whose time-varying mean is the superposition of a small number of oscillatory components, we formulate nonparametric batch spectral analysis as a Bayesian estimation problem. We introduce prior distributions on the time–frequency plane that yield maximum a posteriori (MAP) spectral estimates that are continuous in time yet sparse in frequency. Our spectral decomposition procedure, termed spectrotemporal pursuit, can be efficiently computed using an iteratively reweighted least-squares algorithm and scales well with typical data lengths. We show that spectrotemporal pursuit works by applying to the time series a set of data-derived filters. Using a link between Gaussian mixture models, ℓ[subscript 1] minimization, and the expectation–maximization algorithm, we prove that spectrotemporal pursuit converges to the global MAP estimate. We illustrate our technique on simulated and real human EEG data as well as on human neural spiking activity recorded during loss of consciousness induced by the anesthetic propofol. For the EEG data, our technique yields significantly denoised spectral estimates that have significantly higher time and frequency resolution than multitaper spectral estimates. For the neural spiking data, we obtain a new spectral representation of neuronal firing rates. Spectrotemporal pursuit offers a robust spectral decomposition framework that is a principled alternative to existing methods for decomposing time series into a small number of smooth oscillatory components.en_US
dc.description.sponsorshipNational Institutes of Health (U.S.) (Transformative Research Award GM 104948)en_US
dc.description.sponsorshipNational Institutes of Health (U.S.) (New Innovator Award R01-EB006385)en_US
dc.language.isoen_US
dc.publisherNational Academy of Sciences (U.S.)en_US
dc.relation.isversionofhttp://dx.doi.org/10.1073/pnas.1320637111en_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.sourceNational Academy of Sciences (U.S.)en_US
dc.titleRobust spectrotemporal decomposition by iteratively reweighted least squaresen_US
dc.typeArticleen_US
dc.identifier.citationBa, Demba, Behtash Babadi, Patrick L. Purdon, and Emery N. Brown. “Robust Spectrotemporal Decomposition by Iteratively Reweighted Least Squares.” Proceedings of the National Academy of Sciences 111, no. 50 (December 2, 2014): E5336–E5345.en_US
dc.contributor.departmentInstitute for Medical Engineering and Scienceen_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Brain and Cognitive Sciencesen_US
dc.contributor.mitauthorBa, Demba E.en_US
dc.contributor.mitauthorBrown, Emery N.en_US
dc.relation.journalProceedings of the National Academy of Sciencesen_US
dc.eprint.versionFinal published versionen_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dspace.orderedauthorsBa, Demba; Babadi, Behtash; Purdon, Patrick L.; Brown, Emery N.en_US
dc.identifier.orcidhttps://orcid.org/0000-0003-2668-7819
mit.licensePUBLISHER_POLICYen_US


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