Identification of kronecker-structured dictionaries: An asymptotic analysis

Abstract

The focus of this work is on derivation of conditions for asymptotic recovery of Kronecker-structured dictionaries underlying second-order tensor data. Given second-order tensor observations (equivalently, matrix-valued data samples) that are generated using a Kronecker-structured dictionary and sparse coefficient tensors, conditions on the dictionary and coefficient distribution are derived that enable asymptotic recovery of the individual coordinate dictionaries comprising the Kronecker dictionary within a local neighborhood of the true model. These conditions constitute the first step towards understanding the sample complexity of Kronecker-structured dictionary learning for second- and higher-order tensor data.