Appears in collection : Statistical Modeling for Shapes and Imaging

We propose a new ultrasparse graphical model for representing time varying images, and other multiway data, based on a Kronecker sum representation of the spatio-temporal inverse covariance matrix. This statistical model decomposes the inverse covariance into a linear Kronecker sum representation with sparse Kronecker factors. Under the assumption that the multiway observations are matrix-normal the l1 sparsity regularized log-likelihood function is convex and admits significantly faster statistical rates of convergence than other sparse matrix normal algorithms such as graphical lasso or Kronecker graphical lasso. We will illustrate the method on meteoroligical and MRI imagery to demonstrate the ability of the model to capture sparse structure with few samples. This is joint work with Kristjan Greenewald and Shuheng Zhou.