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. Rauhut, Holger; Schwab, Christoph: Compressive sensing Petrov-Galerkin approximation of high-dimensional parametric operator equations (2017)
  2. Beck, Amir; Hallak, Nadav: On the minimization over sparse symmetric sets: projections, optimality conditions, and algorithms (2016)
  3. Fountoulakis, Kimon; Gondzio, Jacek: Performance of first- and second-order methods for $\ell_1$-regularized least squares problems (2016)
  4. Fountoulakis, Kimon; Gondzio, Jacek: A second-order method for strongly convex $\ell _1$-regularization problems (2016)
  5. Giryes, Raja: Sampling in the analysis transform domain (2016)
  6. Giuliani, Marc-Antoine: Orthogonal one step greedy procedure for heteroscedastic linear models (2016)
  7. Gottlieb, Lee-Ad; Neylon, Tyler: Matrix sparsification and the sparse null space problem (2016)
  8. Iwen, Mark A.; Viswanathan, Aditya; Wang, Yang: Fast phase retrieval from local correlation measurements (2016)
  9. Nikolova, Mila: Relationship between the optimal solutions of least squares regularized with $\ell_0$-norm and constrained by $k$-sparsity (2016)
  10. Raj, Raghu G.: A hierarchical Bayesian-MAP approach to inverse problems in imaging (2016)
  11. Temlyakov, Vladimir: Lebesgue-type inequalities for greedy approximation (2016)
  12. Vanderbei, Robert; Lin, Kevin; Liu, Han; Wang, Lie: Revisiting compressed sensing: exploiting the efficiency of simplex and sparsification methods (2016)
  13. Wang, Fasong; Li, Rui; Wang, Zhongyong; Zhang, Jiankang: Compressed blind signal reconstruction model and algorithm (2016)
  14. Adalsteinsson, Gudmundur F.; Kevlahan, Nicholas K.-R.: Compressive sampling for energy spectrum estimation of turbulent flows (2015)
  15. Boche, Holger; Calderbank, Robert; Kutyniok, Gitta; Vybíral, Jan: A survey of compressed sensing (2015)
  16. Bourgain, Jean; Dirksen, Sjoerd; Nelson, Jelani: Toward a unified theory of sparse dimensionality reduction in Euclidean space (2015)
  17. Cai, Yun; Li, Song: Convergence analysis of projected gradient descent for Schatten-$p$ nonconvex matrix recovery (2015)
  18. Chou, Evan; Güntürk, C.Sinan; Krahmer, Felix; Saab, Rayan; Yılmaz, Özgür: Noise-shaping quantization methods for frame-based and compressive sampling systems (2015)
  19. Eftekhari, Armin; Wakin, Michael B.: New analysis of manifold embeddings and signal recovery from compressive measurements (2015)
  20. Eftekhari, Armin; Yap, Han Lun; Rozell, Christopher J.; Wakin, Michael B.: The restricted isometry property for random block diagonal matrices (2015)

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