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. Brugiapaglia, Simone; Nobile, Fabio; Micheletti, Stefano; Perotto, Simona: A theoretical study of compressed solving for advection-diffusion-reaction problems (2018)
  2. Saab, Rayan; Wang, Rongrong; Yılmaz, Özgür: Quantization of compressive samples with stable and robust recovery (2018)
  3. Adamo, Alessandro; Grossi, Giuliano; Lanzarotti, Raffaella; Lin, Jianyi: Sparse decomposition by iterating Lipschitzian-type mappings (2017)
  4. Bouwmans, Thierry; Sobral, Andrews; Javed, Sajid; Jung, Soon Ki; Zahzah, El-Hadi: Decomposition into low-rank plus additive matrices for background/foreground separation: a review for a comparative evaluation with a large-scale dataset (2017)
  5. Eghbali, Reza; Fazel, Maryam: Decomposable norm minimization with proximal-gradient homotopy algorithm (2017)
  6. Fu, Yusheng; Liu, Shanshan; Ren, Chunhui: Adaptive step-size matching pursuit algorithm for practical sparse reconstruction (2017)
  7. Haviv, Ishay; Regev, Oded: The restricted isometry property of subsampled Fourier matrices (2017)
  8. Hu, Jun; Zhang, Shudao: Global sensitivity analysis based on high-dimensional sparse surrogate construction (2017)
  9. Iwen, Mark; Viswanathan, Aditya; Wang, Yang: Robust sparse phase retrieval made easy (2017)
  10. Jie, Yingmo; Guo, Cheng; Fu, Zhangjie: Newly deterministic construction of compressed sensing matrices via singular linear spaces over finite fields (2017)
  11. Krol, Jakub; Wynn, Andrew: Dynamic reconstruction and data reconstruction for subsampled or irregularly sampled data (2017)
  12. Rauhut, Holger; Schwab, Christoph: Compressive sensing Petrov-Galerkin approximation of high-dimensional parametric operator equations (2017)
  13. Satpathi, Siddhartha; Chakraborty, Mrityunjoy: On the number of iterations for convergence of CoSaMP and subspace pursuit algorithms (2017)
  14. Stanković, Ljubiša; Daković, Miloš; Vujović, Stefan: Reconstruction of sparse signals in impulsive disturbance environments (2017)
  15. Wang, Dan; Zhang, Zhuhong: Generalized sparse recovery model and its neural dynamical optimization method for compressed sensing (2017)
  16. Wang, Yang; Xiang, Xiuqiao; Zhou, Shunping; Luo, Zhongwen; Fang, Fang: Compressed sensing based on trust region method (2017)
  17. Yang, Enpin; Zhang, Tianhong; Yan, Xiao; Wang, Qian; Qin, Kaiyu: Arbitrary block-sparse signal reconstruction based on incomplete single measurement vector (2017)
  18. Zhang, Na; Li, Qia: On optimal solutions of the constrained $\ell_0$ regularization and its penalty problem (2017)
  19. Zhang, Yujie; Zhang, Shizhong; Qi, Rui: Compressed sensing construction for underdetermined source separation (2017)
  20. Zhu, Zhihui; Wakin, Michael B.: Approximating sampled sinusoids and multiband signals using multiband modulated DPSS dictionaries (2017)

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