This project aims to advance neural data analysis and image processing by exploiting the structure in multivariate phase representations. Combining insights from neural computation with advances in multivariate statistics, mathematical signal analysis, and machine learning, the project aims to build multivariate statistical models of angular variables that capture the dependencies between complex and hypercomplex phase variables. Recursive estimation techniques will be developed to allow for optimal estimation of distributions from noisy data and prediction of their temporal evolution. The models developed in this proposal will be applied to current problems in neuroscience and image processing.
As a foundation for the application domains, a recently developed method for estimating the parameters of stationary multivariate phase distributions will be generalized to situations in which the parameters are time-varying and the measurements are noisy, linear mixtures of the underlying sources. A recursive filtering model, similar to the classical Kalman filter, will be developed, that produces an optimal online estimate of latent phase variables in response to a sequence of noisy measurements.
In the first application domain, this model will be used to infer connectivity and temporal interactions among populations of neural oscillators from physiological measurements. The model will also be used to detect transient changes in connectivity by utilizing a mixture model of phase dynamics. These estimation techniques will be evaluated on simulated data and then applied to the analysis of neurophysiological recordings to better elucidate network dynamics.
In the application domain of natural image statistics, the model will be extended to handle hypercomplex phase variables in order to model the phase and orientation of edges in natural images, which contain rich information that may be exploited for image analysis and object recognition. The project aims to develop a model that describes the spatial dependencies among these variables as a nonlinear mixture of multivariate phase distributions.
https://redwood.berkeley.edu/wiki/NSF_Funded_Research
