Tensor Low Rank Modeling and Its Applications in Signal Processing

TL;DR

This paper discusses tensor low rank modeling for multidimensional signals, emphasizing its mathematical foundations, advantages, and diverse applications in signal processing tasks like denoising and object detection.

Contribution

It provides a comprehensive introduction to linear transform based tensor algebra and demonstrates its application in low rank approximation for various signal processing problems.

Findings

Low rank tensor approximation effectively captures signal structures.

Tensor methods improve performance in denoising and classification.

Case studies illustrate practical benefits in multiple applications.

Abstract

Modeling of multidimensional signal using tensor is more convincing than representing it as a collection of matrices. The tensor based approaches can explore the abundant spatial and temporal structures of the mutlidimensional signal. The backbone of this modeling is the mathematical foundations of tensor algebra. The linear transform based tensor algebra furnishes low complex and high performance algebraic structures suitable for the introspection of the multidimensional signal. A comprehensive introduction of the linear transform based tensor algebra is provided from the signal processing viewpoint. The rank of a multidimensional signal is a precious property which gives an insight into the structural aspects of it. All natural multidimensional signals can be approximated to a low rank signal without losing significant information. The low rank approximation is beneficial in many signal processing applications such as denoising, missing sample estimation, resolution enhancement, classification, background estimation, object detection, deweathering, clustering and much more applications. Detailed case study of the ways and means of the low rank modeling in the above said signal processing applications are also presented.