Year: 2025
Type: article
Abstract: This note demonstrates that we can stably recover rank-rToeplitz matrix$\pmb {X}\in \mathbb {R}^{n\times n}$from a number of rank-one subgaussian measurements on the order of$r\log ^{2} n$with an exponentially decreasing failure probability by employing a nuclear norm minimization program. Our approach utilizes descent cone analysis through Mendelson’s small ball method with the Toeplitz constraint. The key ingredient is to determine the spectral norm of the random matrix of the Toeplitz structure, which may be of independent interest. This improves upon earlier analyses and resolves the conjecture in Chen et al. (IEEE Transactions on Information Theory, 61(7):4034–4059, 2015).
Authors: Gao Huang, Song Li
Institution: Zhejiang University
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Awards: 基于傅立叶分析的压缩感知理论研究, G420315194
OpenAlex ID: W4408565558