Phase transition and noise sensitivity of ℓp-minimization for 0 ≤ p ≤ 1

@article{Weng2016PhaseTA,
  title={Phase transition and noise sensitivity of ℓp-minimization for 0 ≤ p ≤ 1},
  author={Haolei Weng and Le Zheng and Arian Maleki and Xiaodong Wang},
  journal={2016 IEEE International Symposium on Information Theory (ISIT)},
  year={2016},
  pages={675-679}
}
Recovering a sparse vector x<sub>0</sub> ∈ ℝ<sup>N</sup> from its noisy linear observations, y ∈ ℝ<sup>n</sup> with y = Ax<sub>0</sub> + w, has been the central problem of compressed sensing. One of the classes of recovery algorithms that has attracted attention is the class of ℓ<sub>p</sub>-regularized least squares (LPLS) that seeks the minimum of 1/2 ∥y - Ax∥<sub>2</sub><sup>2</sup> + λ∥x∥<sub>p</sub><sup>p</sup> for p ∈ [0, 1]. In this paper we employ the Replica method<sup>1</sup> from… CONTINUE READING

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