Abstract
Recently, based on a new tensor algebraic framework for third-order tensors, the tensor singular value decomposition (t-SVD) and its associated tubal rank definition have shed new light on low-rank tensor modeling. Its applications to robust image/video recovery and background modeling show promising performance due to its superior capability in modeling cross-channel/frame information. Under the t-SVD framework, we propose a new tensor norm called tensor spectral k-support norm (TSP-k) by an alternative convex relaxation. As an interpolation between the existing tensor nuclear norm (TNN) and tensor Frobenius norm (TFN), it is able to simultaneously drive minor singular values to zero to induce low-rankness, and to capture more global information for better preserving intrinsic structure. We provide the proximal operator and the polar operator for the TSP-k norm as key optimization blocks, along with two showcase optimization algorithms for medium-and large-size tensors. Experiments on synthetic, image and video datasets in medium and large sizes, all verify the superiority of the TSP-k norm and the effectiveness of both optimization methods in comparison with the existing counterparts.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.