Tensor Decompositions for Hyperspectral Data Processing in Remote Sensing: A Comprehensive Review

Abstract

Owing to the rapid development of sensor technology, hyperspectral (HS) remote sensing (RS) imaging has provided a significant amount of spatial and spectral information for the observation and analysis of the Earth's surface at a distance of data acquisition devices, such as aircraft, spacecraft, and satellite. The recent advancement and even revolution of the HS RS technique offer opportunities to realize the full potential of various applications, while confronting new challenges for efficiently processing and analyzing the enormous HS acquisition data. Due to the maintenance of the 3-D HS inherent structure, tensor decomposition has aroused widespread concern and research in HS data processing tasks over the past decades. In this article, we aim at presenting a comprehensive overview of tensor decomposition, specifically contextualizing the five broad topics in HS data processing, and they are HS restoration, compressed sensing, anomaly detection, superresolution, and spectral unmixing. For each topic, we elaborate on the remarkable achievements of tensor decomposition models for HS RS with a pivotal description of the existing methodologies and a representative exhibition on the experimental results. As a result, the remaining challenges of the follow-up research directions are outlined and discussed from the perspective of the real HS RS practices and tensor decomposition merged with advanced priors and even with deep neural networks. This article summarizes different tensor decomposition-based HS data processing methods and categorizes them into different classes from simple adoptions to complex combinations with other Manuscript received XX, 2022; revised XX, 2022.

Nonnegative Block-Term Decomposition with the β-Divergence: Joint Data Fusion and Blind Spectral Unmixing

“…As done in previous works (see [11]), we consider the following model providing the links between Y and its two degradations Y 1 and Y 2 .…”

“…In this appendix, we give the closed-form expressions for the multiplicative updates of B and C, similarly to (11). T .…”

“…The works of [8], [9] formulate the HSR problem as a coupled canonical polyadic (CP) decomposition, while a coupled multilinear Tucker decomposition is used in [10]. See [11] for an overview of tensor methods for hyperspectral data processing. However, the factors of these decompositions lack physical interpretation, and thus the aforementioned methods cannot be used for unmixing.…”