Transform-based tensor singular value decomposition in multidimensional image recovery

Due to the limitation of imaging conditions, observed multidimensional images (e.g., color images, video, and multispectral/hyperspectral images) are unavoidably incomplete or corrupted, hindering subsequent applications. Multidimensional image recovery, which infers the underlying multidimensional image from the degraded observation, is a fundamental problem in low-level vision. Recently, tensor singular value decomposition (t-SVD) emerged as a powerful multilinear framework for preserving the intrinsic structure of multidimensional images. In this chapter, we revisit the establishment of the t-SVD framework and some recent advances based on this approach. Next, the recent development of transform-based t-SVD for multidimensional image recovery is reviewed. Additionally, some numerical examples are provided. Finally, we summarize the trend of the developments for multidimensional image recovery within the t-SVD framework and suggest possible directions for future research.