1 Introduction
1.1 Necessity of HSI Restoration
2 Outline and Theoretical Foundations
2.1 Mathematical Preliminaries
2.2 Low-Rank Tensor Approximation
3 LRTA for HSI Denoising
4 LRTA for HS-MS Fusion
5 LRTA for HSI Destriping
6 LRTA for HSI Inpainting
7 LRTA for HSI Deblurring
8 LRTA for HSI Super-resolution
9 Open Issues and Challenges
10 Conclusions