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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  1. Eghbali, Reza; Fazel, Maryam: Decomposable norm minimization with proximal-gradient homotopy algorithm (2017)
  2. Hu, Jun; Zhang, Shudao: Global sensitivity analysis based on high-dimensional sparse surrogate construction (2017)
  3. Iwen, Mark; Viswanathan, Aditya; Wang, Yang: Robust sparse phase retrieval made easy (2017)
  4. Rauhut, Holger; Schwab, Christoph: Compressive sensing Petrov-Galerkin approximation of high-dimensional parametric operator equations (2017)
  5. Wang, Yang; Xiang, Xiuqiao; Zhou, Shunping; Luo, Zhongwen; Fang, Fang: Compressed sensing based on trust region method (2017)
  6. Zhang, Na; Li, Qia: On optimal solutions of the constrained $\ell_0$ regularization and its penalty problem (2017)
  7. Beck, Amir; Hallak, Nadav: On the minimization over sparse symmetric sets: projections, optimality conditions, and algorithms (2016)
  8. Bouchot, Jean-Luc; Foucart, Simon; Hitczenko, Pawel: Hard thresholding pursuit algorithms: number of iterations (2016)
  9. Deepa, K.G.; Ambat, Sooraj K.; Hari, K.V.S.: Fusion of sparse reconstruction algorithms for multiple measurement vectors (2016)
  10. De, Parthapratim; Satija, Udit: Sparse representation for blind spectrum sensing in cognitive radio: a compressed sensing approach (2016)
  11. Fountoulakis, Kimon; Gondzio, Jacek: A second-order method for strongly convex $\ell _1$-regularization problems (2016)
  12. Fountoulakis, Kimon; Gondzio, Jacek: Performance of first- and second-order methods for $\ell_1$-regularized least squares problems (2016)
  13. Giryes, Raja: Sampling in the analysis transform domain (2016)
  14. Giuliani, Marc-Antoine: Orthogonal one step greedy procedure for heteroscedastic linear models (2016)
  15. Gottlieb, Lee-Ad; Neylon, Tyler: Matrix sparsification and the sparse null space problem (2016)
  16. Han, Yu; Du, Huiqian; Lam, Fan; Mei, Wenbo; Fang, Liping: Image reconstruction using analysis model prior (2016)
  17. Iwen, Mark A.; Viswanathan, Aditya; Wang, Yang: Fast phase retrieval from local correlation measurements (2016)
  18. Nikolova, Mila: Relationship between the optimal solutions of least squares regularized with $\ell_0$-norm and constrained by $k$-sparsity (2016)
  19. Raj, Raghu G.: A hierarchical Bayesian-MAP approach to inverse problems in imaging (2016)
  20. Temlyakov, Vladimir: Lebesgue-type inequalities for greedy approximation (2016)

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