A Block Term Decomposition Model Based Algorithm for Tensor Completion of Multidimensional Harmonic Signals

TL;DR

This paper introduces a tensor completion algorithm based on block term decomposition (BTD) for multidimensional harmonic signals, offering a more flexible modeling approach than traditional methods, validated through simulations and real-world applications.

Contribution

It proposes a novel BTD-based tensor completion method that captures complex harmonic relationships, improving over existing CPD-based techniques.

Findings

Effective in numerical simulations

Successful application to Sub-6GHz CSI completion

Outperforms traditional CPD-based methods

Abstract

We consider tensor data completion of an incomplete observation of multidimensional harmonic (MH) signals. Unlike existing tensor-based techniques for MH retrieval (MHR), which mostly adopt the canonical polyadic decomposition (CPD) to model the simple "one-to-one" correspondence among harmonics across difference modes, we herein use the more flexible block term decomposition (BTD) model that can be used to describe the complex mutual correspondences among several groups of harmonics across different modes. An optimization principle that aims to fit the BTD model in the least squares sense, subject to rank minimization of hankelized MH components, is set up for the tensor completion task, and an algorithm based on alternating direction method of multipliers is proposed, of which the effectiveness and applicability are validated through both numerical simulations and an application in Sub-6GHz channel state information (CSI) completion.