title: Robust spectrotemporal decomposition by iteratively reweighted least squares.
abstract: Classical 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, l1 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.
authors.affiliation: Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139; Department of Anesthesia, Critical Care and Pain Medicine, Massachusetts General Hospital, Boston, MA 02114; demba@mit.edu.
authors.forename: Demba
authors.initials: D
authors.lastname: Ba
authors.affiliation: Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20740;
authors.forename: Behtash
authors.initials: B
authors.lastname: Babadi
authors.affiliation: Department of Anesthesia, Critical Care and Pain Medicine, Massachusetts General Hospital, Boston, MA 02114; Harvard Medical School, Boston, MA 02115; and.
authors.forename: Patrick L
authors.initials: PL
authors.lastname: Purdon
authors.affiliation: Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139; Department of Anesthesia, Critical Care and Pain Medicine, Massachusetts General Hospital, Boston, MA 02114; Harvard Medical School, Boston, MA 02115; and Institute for Medical Engineering and Science, Massachusetts Institute of Technology, Cambridge, MA 02139.
authors.forename: Emery N
authors.initials: EN
authors.lastname: Brown
mesh_terms: D000200:Action Potentials / Q000502:physiology; D000465:Algorithms; D001499:Bayes Theorem; D003627:Data Interpretation, Statistical; D004569:Electroencephalography; D006801:Humans; D016018:Least-Squares Analysis; D012815:Signal Processing, Computer-Assisted; D013997:Time Factors
keywords: dynamics; neural signal processing; recursive estimation; spectral decomposition; structured sparsity