TY - CHAP
T1 - Transform-based tensor singular value decomposition in multidimensional image recovery
AU - Jiang, Tai Xiang
AU - Ng, Michael K.
AU - Zhao, Xi Le
N1 - This work was supported in part by the National Natural Science Foundation of China under Grants 12001446, 61876203, and 61772003; in part by the Key Project of Applied Basic Research in Sichuan Province under Grant 2020YJ0216; in part by the Applied Basic Research Project of Sichuan Province under Grant 2021YJ0107; in part by the National Key Research and Development Program of China under Grant 2020YFA0714001; in part by the Fundamental Research Funds for the Central Universities under Grant JBK2102001; and in part by the HKRGC GRF under Grants 12300218, 12300519, 17201020 and 17300021.
Publisher Copyright:
© 2022 Elsevier Inc. All rights reserved.
PY - 2021/10/21
Y1 - 2021/10/21
N2 - 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.
AB - 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.
KW - Discrete Fourier transform
KW - Linear transform
KW - Multidimensional image recovery
KW - Tensor nuclear norm (TNN)
KW - Tensor singular value decomposition (t-SVD)
UR - https://shop.elsevier.com/books/tensors-for-data-processing/liu/978-0-12-824447-0
UR - http://www.scopus.com/inward/record.url?scp=85129629829&partnerID=8YFLogxK
U2 - 10.1016/B978-0-12-824447-0.00008-X
DO - 10.1016/B978-0-12-824447-0.00008-X
M3 - Chapter
AN - SCOPUS:85129629829
SN - 9780128244470
SP - 31
EP - 60
BT - Tensors for Data Processing
A2 - Liu, Yipeng
PB - Elsevier
ER -