Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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STABLE AND ROBUST ℓp-CONSTRAINED COMPRESSIVE SENSING RECOVERY VIA ROBUST WIDTH PROPERTY

  • Yu, Jun (Department of Mathematics and Mathematical Statistics Umea University) ;
  • Zhou, Zhiyong (Department of Mathematics and Mathematical Statistics Umea University)
  • Received : 2018.05.09
  • Accepted : 2018.12.06
  • Published : 2019.05.01
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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 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

Acknowledgement

Supported by : Swedish Research Council

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