Open AccessFundamental Lower Bounds on Number of Random Measurements for Structured Matrix Signal Reconstruction
Author(s) -
Yuan Tian,
Xin Huang
Publication year - 2020
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 - 10.1088/1742-6596/1624/3/032020
Subject(s) - mathematics , matrix (chemical analysis) , signal (programming language) , algorithm , random matrix , convex optimization , signal reconstruction , matrix completion , tensor (intrinsic definition) , multivariate random variable , mathematical optimization , regular polygon , upper and lower bounds , signal processing , computer science , random variable , mathematical analysis , statistics , pure mathematics , geometry , physics , telecommunications , radar , eigenvalues and eigenvectors , materials science , quantum mechanics , composite material , gaussian , programming language
This paper deals with the problem of robustly reconstructing n -by- n structured matrix signal via convex optimization in random setting. The traditional vector signal model is extended to matrix model. By means of a generalized matrix width estimation and sub-differential analysis, fundamental lower bounds on number of random measurements to guarantee high successful reconstruction probability are established. In comparison with most current works, these bounds are tighter and the methods are more suitable to be generalized to dealing with high-order tensor signals.