A multivariate, multitaper approach to detecting and estimating harmonic response in cortical optical imaging data

The efficiency and accuracy of cortical maps from optical imaging experiments have been improved using periodic stimulation protocols. The resulting data analysis requires the detection and estimation of periodic information in a multivariate dataset. To date, these analyses have relied on discrete Fourier transform (DFT) sinusoid estimates. Multitaper methods have become common statistical tools in the analysis of univariate time series that can give improved estimates. Here, we extend univariate multitaper harmonic analysis methods to the multivariate, imaging context. Given the hypothesis that a coherent oscillation across many pixels exists within a specified bandwidth, we investigate the problem of its detection and estimation in noisy data by constructing Hotelling's generalized T2-test. We then extend the investigation of this problem in two contexts, that of standard canonical variate analysis (CVA) and that of generalized indicator function analysis (GIFA) which is often more robust in extracting a signal in spatially correlated noise. We provide detailed information on the fidelities of the mean estimates found with our methods and comparison with DFT estimates. Our results indicate that GIFA provides particularly good estimates of harmonic signals in spatially correlated noise and is useful for detecting small amplitude harmonic signals in applications such as biological imaging measurements where spatially correlated noise is common. We demonstrate the power of our methods with an optical imaging dataset of the periodic response to a periodically rotating oriented drifting grating stimulus experiment in cat visual cortex.