Journal of the
Korean Mathematical Society JKMS

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

Supported by: This work is supported by the Swedish Research Council grant (Reg.No. 340-2013-5342).