Stable and robust $\ell_p$-constrained compressive sensing recovery via robust width property
J. Korean Math. Soc. 2019 Vol. 56, No. 3, 689-701
https://doi.org/10.4134/JKMS.j180321
Published online 2019 May 01
Jun Yu, Zhiyong Zhou
Ume{\aa} University; Ume{\aa} University
Abstract : We study the recovery results of $\ell_p$-constrained compressive sensing (CS) with $p\geq 1$ via robust width property and determine conditions on the number of measurements for standard Gaussian matrices under which the property holds with high probability. Our paper extends the existing results in Cahill and Mixon \cite{cm} from $\ell_2$-constrained CS to $\ell_p$-constrained case with $p\geq 1$ and complements the recovery analysis for robust CS with $\ell_p$ loss function.
Keywords : compressive sensing, robust width property, robust null space property, restricted isometry property
MSC numbers : 94A12, 94A20
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