Open AccessFundamental Lower Bounds on Number of Random Measurements for 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 - 10.1088/1742-6596/1927/1/012005
Subject(s) - tensor (intrinsic definition) , mathematics , signal (programming language) , signal reconstruction , signal processing , tensor contraction , algorithm , regular polygon , convex optimization , compressed sensing , mathematical optimization , computer science , mathematical analysis , pure mathematics , exact solutions in general relativity , geometry , digital signal processing , computer hardware , programming language
This paper deals with a fundamental aspect of the problem of robustly reconstructing sparse tensor signals via convex optimization in random setting. The traditional vector signal model is extended to tensor model and tensor-space based probability analysis methods are applied to establish the critical results. In particular, by means of an innovative tensor width estimation and asymptotic convex geometric analysis, fundamental lower bounds on number of random measurements to guarantee high successful reconstruction probability are established. In comparison with most current works based on vector signal model (1-order tensor), these bounds establish foundations to develop effective algorithms for reconstructing high-order sparse tensor signals which are emerging in various data-intensive intelligent signal processing applications.