Approximating Symmetric Positive Semidefinite Tensors of Even Order

• Authors: Angelos Barmpoutis;Jeffrey Ho;Baba C. Vemuri
• Venue: SIAM Journal on Imaging Sciences
• Year: 2012

Tensors of various orders can be used for modeling physical quantities such as strain and diffusion as well as curvature and other quantities of geometric origin. Depending on the physical properties of the modeled quantity, the estimated tensors are often required to satisfy the positivity constraint, which can be satisfied only with tensors of even order. Although the space $\mathcal{P}_0^{2m}$ of $2m$th-order symmetric positive semidefinite tensors is known to be a convex cone, enforcing positivity constraint directly on $\mathcal{P}_0^{2m}$ is usually not straightforward computationally because there is no known analytic description of $\mathcal{P}_0^{2m}$ for $m1$. In this paper, we propose a novel approach for enforcing the positivity constraint on even-order tensors by approximating the cone $\mathcal{P}_0^{2m}$ for the cases $0