Abstract
A central problem in compressed sensing is the construction of sensing matrices. In this paper, we show how to construct sensing matrices by using semilattices, and give many examples of sensing matrices constructed from specific semilattices. Moreover, we show that the new construction for some examples with small parameters gives better sensing matrices compared with previously known constructions.
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Bourgain J, Dilworth S, Ford K, Konyagin S, Kutzarova D (2011) Explicit constructions of RIP matrices and related problems. Duke Math J 159:145–185
Candès E, Tao T (2005) Decoding by linear programming. IEEE Trans Inf Theory 51:4203–4215
Candès E, Tao T (2006) Near-optimal signal recovery fromrandom projections: universal encoding strategies. IEEE Trans Inf Theory 52:5406–5425
Candès E, Romberg J, Tao T (2006) Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inf Theory 52:489–509
Cohen A, Dahmen W, DeVore R (2009) Compressed sensing and best \(k\)-term approximation. J Am Math Soc 22:211–231
DeVore R (2007) Deterministic constructions of compressed sensing matrices. J Complex 23:918–925
Donoho D (2006) Compressed sensing. IEEE Trans Inf Theory 52:1289–1306
Gao S, Guo J, Liu W (2007) Lattices generated by strongly closed subgraphs in \(d\)-bounded distance-regular graphs. Eur J Comb 28:1800–1813
Guo J, Ma J, Wang K (2013) Erdős–Ko–Rado theorems in certain semilattices. Sci China Math 56:2393–2407
Guo J, Wang K, Weng C (2014) Pooling semilattices and non-adaptive pooling designs. Discrete Math 320:64–72
Huang T, Weng C (2004) Pooling spaces and non-adaptive pooling designs. Discrete Math 282:163–169
Li S, Ge G (2014) Deterministic construction of sparse sensing matrices via finite geometry. IEEE Trans Signal Process 62:2850–2859
Li S, Gao F, Ge G, Zhang S (2012) Deterministic construction of compressed sensing matrices via algebraic curves. IEEE Trans Inf Theory 58:5035–5041
Welch L (1974) Lower bounds on the maximum cross correlation of signals. IEEE Trans Inf Theory 20:397–399
Acknowledgements
This research is supported by NSF of China (11271047, 11401282), NSF of Hebei Province (A2016408016), the Fund for Hundreds of Excellent Innovative Talents in Higher Education of Hebei Province (BR2-235) and Foundation of Hebei Education Department (No. YQ2014018).
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Guo, J., Liu, J. Deterministic construction of compressed sensing matrices based on semilattices. J Comb Optim 35, 148–161 (2018). https://doi.org/10.1007/s10878-017-0162-9
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DOI: https://doi.org/10.1007/s10878-017-0162-9