Speaker: Ranjan Maitra, Professor, Iowa State University Department of Statistics

Title: Fourier tensor-variate distributions for modeling nonstationarity in high-resolution imaging and other applications

Abstract: Data in the form of arrays (or tensors) are ubiquitous in imaging and other contexts and are usually analyzed using methodologies that impose simplified structures on the tensor-variate structure of their mean or variance. We introduce the Fourier tensor-variate (FTV) family of distributions, with covariance matrices whose eigenvectors are specified by the real discrete Fourier transform (RDFT). An attractive feature of this covariance specification is its ability to capture nonstationarity while maintaining periodicity. Further, a random tensor with the correspondingly named Fourier covariance structure is element-wise independent after applying an inverse RDFT. Therefore, traditional univariate distributions can be extended to their FTV counterparts, with inference on the induced FTV family mirroring that of their univariate cousins, while partaking of the computational benefits of using the Fourier transform. Indeed, the estimation of the high-dimensional tensor covariance is delegated to the estimation of its eigenvalues, naturally allowing for principal component analysis (PCA) to summarize variability. Our methods are evaluated in simulations involving bitmap images and illustrated on applications involving digital imaging and precision agriculture.

This work is joint with Carlos Llosa-Vite of Sandia National Laboratories.