CoSaMP: Iterative signal recovery from incomplete and inaccurate samples. Compressive sampling offers a new paradigm for acquiring signals that are compressible with respect to an orthonormal basis. The major algorithmic challenge in compressive sampling is to approximate a compressible signal from noisy samples. This paper describes a new iterative recovery algorithm called CoSaMP that delivers the same guarantees as the best optimization-based approaches. Moreover, this algorithm offers rigorous bounds on computational cost and storage. It is likely to be extremely efficient for practical problems because it requires only matrix-vector multiplies with the sampling matrix. For compressible signals, the running time is just $O(Nlog ^{2}N)$, where $N$ is the length of the signal.

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  4. Zhang, Na; Li, Qia: On optimal solutions of the constrained $\ell_0$ regularization and its penalty problem (2017)
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  8. Fountoulakis, Kimon; Gondzio, Jacek: Performance of first- and second-order methods for $\ell_1$-regularized least squares problems (2016)
  9. Giryes, Raja: Sampling in the analysis transform domain (2016)
  10. Giuliani, Marc-Antoine: Orthogonal one step greedy procedure for heteroscedastic linear models (2016)
  11. Gottlieb, Lee-Ad; Neylon, Tyler: Matrix sparsification and the sparse null space problem (2016)
  12. Han, Yu; Du, Huiqian; Lam, Fan; Mei, Wenbo; Fang, Liping: Image reconstruction using analysis model prior (2016)
  13. Iwen, Mark A.; Viswanathan, Aditya; Wang, Yang: Fast phase retrieval from local correlation measurements (2016)
  14. Nikolova, Mila: Relationship between the optimal solutions of least squares regularized with $\ell_0$-norm and constrained by $k$-sparsity (2016)
  15. Raj, Raghu G.: A hierarchical Bayesian-MAP approach to inverse problems in imaging (2016)
  16. Temlyakov, Vladimir: Lebesgue-type inequalities for greedy approximation (2016)
  17. Vanderbei, Robert; Lin, Kevin; Liu, Han; Wang, Lie: Revisiting compressed sensing: exploiting the efficiency of simplex and sparsification methods (2016)
  18. Wang, Fasong; Li, Rui; Wang, Zhongyong; Zhang, Jiankang: Compressed blind signal reconstruction model and algorithm (2016)
  19. Wang, Xin; Zhang, Jun; Ge, Gennian: Deterministic convolutional compressed sensing matrices (2016)
  20. Zeng, Cao; Zhu, Shengqi; Li, Shidong; Liao, Quisheng; Wang, Lanmei: Sparse frame DOA estimations via a rank-one correlation model for low SNR and limited snapshots (2016)

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