B1128
Title: Fourier-structured tensor-variate distributions for high-resolution imaging applications
Authors: Ranjan Maitra - Iowa State University (United States) [presenting]
Carlos Llosa - Sandia National Laboratories (United States)
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. The Fourier tensor-variate (FTV) family of distributions with covariance matrices is introduced, whose eigenvectors are specified by the real discrete Fourier transform (RDFT). An attractive feature of the 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 counterpart, with inference on the induced FTV family mirroring that of their univariate counterparts while enjoying the computational benefits of using the Fourier transform. Indeed, estimating the high-dimensional tensor covariance is delegated to estimating its eigenvalues, naturally allowing principal component analysis (PCA) to summarize variability. The methods are evaluated in simulations involving bitmap images and are illustrated on applications involving digital imaging, precision agriculture, forensic and medical imaging.
