Open AccessOn General Conditions for Uniqueness and Stability of Sparse Tensor Signal Reconstruction
Author(s) -
Yuan Tian,
Xin Huang
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1927/1/012006
Subject(s) - tensor (intrinsic definition) , cartesian tensor , mathematics , uniqueness , convex optimization , tensor field , signal reconstruction , tensor contraction , mathematical optimization , regular polygon , tensor density , computer science , mathematical analysis , signal processing , exact solutions in general relativity , pure mathematics , geometry , telecommunications , radar
This paper deals with a fundamental aspect of the inverse problem of robustly reconstructing sparse tensor signals via convex optimization. The traditional vector signal model is extended to tensor model and tensor-space based convex optimization methods are applied to establish the critical results. In particular, by means of some innovative sub-differential analysis for tensor norms and convex geometric analysis in normed tensor space, sufficient conditions to guarantee uniqueness and stability of sparse tensor signal reconstruction are established. In comparison with most current works based on vector signal model (1-order tensor), these conditions are more general and more applicable to tensor signals. Also will these conditions be helpful for establishing practical algorithms for reconstructing high-order sparse tensor signals which are emerging in various data-intensive intelligent applications.