Flexible construction of measurement matrices in compressed sensing based on extensions of incidence matrices of combinatorial designs

Junying Liang, Haipeng Peng, Lixiang Li, Fenghua Tong and Yixian Yang

Applied Mathematics and Computation, 2022, vol. 420, issue C

Abstract: In signal processing, compressed sensing (CS) can be used to acquire and reconstruct sparse signals. This paper presents a method of combining vertical expansions and horizontal expansions to construct measurement matrices. Firstly, we give a construction of (n,n,n−1,n−1,n−2)-BIBD based on finite set. It is important to estimate recovery performance of measurement matrices in terms of coherence, and it is found that the incidence matrix H of (n,n,n−1,n−1,n−2)-BIBD is not suitable as a measurement matrix in CS. We present an optimal method of combining vertical expansions and horizontal expansions for addressing this problem. These two extensions provide a new perspective for the construction of measurement matrices. Vertical expansions ensure that the matrix has low coherence. Horizontal expansions ensure that the matrix is more suitable as a measurement matrix in CS because of sizes and coherence. Finally, compared with several typical matrices, our matrices have better recovery performance under OMP and IST by the simulation experiments.

Keywords: Compressed sensing; Measurement matrices; Coherence; Vertical expansions; Horizontal expansions (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S009630032100984X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:420:y:2022:i:c:s009630032100984x

DOI: 10.1016/j.amc.2021.126901

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().