TY - JOUR
T1 - Robust spectrotemporal decomposition by iteratively reweighted least squares
JF - Proceedings of the National Academy of Sciences
JO - Proc Natl Acad Sci USA
SP - E5336
LP - E5345
DO - 10.1073/pnas.1320637111
VL - 111
IS - 50
AU - Ba, Demba
AU - Babadi, Behtash
AU - Purdon, Patrick L.
AU - Brown, Emery N.
Y1 - 2014/12/16
UR - http://www.pnas.org/content/111/50/E5336.abstract
N2 - Classical spectral estimation techniques use sliding windows to enforce temporal smoothness of the spectral estimates of signals with time-varying spectrotemporal representations. This widely applied approach is not well-suited to signals that have low-dimensional, highly structured time–frequency representations. We develop a new Bayesian spectral decomposition framework—spectrotemporal pursuit—to compute spectral estimates that are smooth in time and sparse in frequency. We use a statistical interpretation of sparse recovery to derive efficient algorithms for computing spectrotemporal pursuit spectral estimates. We apply spectrotemporal pursuit to achieve a more precise delineation of the oscillatory structure of human electroencephalogram and neural spiking data under propofol general anesthesia. Spectrotemporal pursuit offers a principled alternative to existing methods for decomposing a signal into a small number of oscillatory components.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.
ER -