Stable and robust $\ell_p$-constrained compressive sensing recovery via robust width property

Zhiyong Zhou; Jun Yu

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arXiv · 1705.03810

Stable and robust $\ell_p$-constrained compressive sensing recovery via robust width property

Zhiyong Zhou·Jun Yu

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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 (2014) 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.

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Zhiyong Zhou, Jun Yu. 2017-05-10. Stable and robust $\ell_p$-constrained compressive sensing recovery via robust width property. https://arxiv.org/abs/1705.03810

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