Speaker
Description
Transform-based tensor products, including the T-product and its more general form, namely the higher-order tensor-tensor product, have been widely used in image processing, signal reconstruction, and robotics. While invertible transforms enable tensor computations to be carried out via matrix operations in the transform domain, the resulting storage and computational costs remain prohibitive for high-dimensional tensors. To address this challenge, we leverage tensor decomposition techniques, including tensor train decomposition (TTD) and hierarchical Tucker decomposition (HTD), to accelerate transform-based multilinear algebra. In particular, we develop TTD- and HTD-based formulations for the T-product and its associated algebra by operating directly on the factor matrices or tensors of the decompositions. The framework is further generalized to the higher-order tensor-tensor product and applied to multilinear control problems. We demonstrate the effectiveness of our framework with numerical examples.