Hankel tensor approximation using structured approach

Abstract

The Hankel tensor is an important tool in the field of signal processing, and the low-rank approximation of the Hankel tensor can be used for signal restoration. Aiming at the low rank approximation problem of real Hankel tensor, this paper proves that there is a special form of Vandermonde decomposition for real Hankel tensor. Based on this form of decomposition, a low-rank approximation algorithm is proposed, which can ensure that the result of the approximation is still real Hankel tensor. This paper confirms that the algorithm can solve the optimal Vandermonde rank-one approximation and Vandermonde decomposition, and uses signal denoising as examples to illustrate the effectiveness of the algorithm.