Abstract
A recent result establishing, under restricted isometry conditions, the success of sparse recovery via orthogonal matching pursuit using a number of iterations proportional to the sparsity level is extended to weak orthogonal matching pursuits. The new result also applies to a pure orthogonal matching pursuit, where the index appended to the support at each iteration is chosen to maximize the subsequent decrease of the squared norm of the residual vector.
This work was triggered by the participation of the author to the NSF-supported Workshop in Linear Analysis and Probability at Texas A&M University.
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References
Candès, E.J.: Compressive sampling. In: Proceedings of the International Congress of Mathematicians, Madrid, Spain (2006)
Davenport, M., Wakin, M.: Analysis of orthogonal matching pursuit using the restricted isometry property. IEEE Trans. Inform. Theory 56(9), 4395–4401 (2010)
Donoho, D.L.: Compressed sensing. IEEE Trans. Inform. Theory 52(4), 1289–1306 (2006)
Foucart, S.: Hard thresholding pursuit: An algorithm for compressive sensing. SIAM J. Numer. Anal. 49(6), 2543–2563 (2011)
Liu, E., Temlyakov, V.: Orthogonal Super Greedy Algorithm and Applications in Compressed Sensing. IEEE Trans. Inform. Theory 58(4), 2040–2047 (2012)
Maleh, R.: Improved RIP Analysis of Orthogonal Matching Pursuit. CoRR abs/1102.4311 (2011)
Mallat, S.G., Zhang, Z.: Matching pursuits with time-frequency dictionaries. IEEE Trans. Signal Process. 41(12), 3397–3415 (1993)
Mo, Q., Shen, Y.: A Remark on the Restricted Isometry Property in Orthogonal Matching Pursuit. IEEE Trans. Inform. Theory 58(6), 3654–3656 (2012)
Rauhut, H.: On the impossibility of uniform sparse reconstruction using greedy methods. Sampling Theory Signal Image Process. 7(2), 197–215 (2008)
Tropp, J.: Greed is good: Algorithmic results for sparse approximation. IEEE Trans. Inform. Theory 50(10), 2231–2242 (2004)
Zhang, T.: Sparse recovery with orthogonal matching pursuit under RIP. IEEE Trans. Inform. Theory 57(9), 6215–6221 (2011)
Acknowledgements
The author is supported by the NSF grant DMS-1120622.
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Foucart, S. (2012). Stability and Robustness of Weak Orthogonal Matching Pursuits. In: Bilyk, D., De Carli, L., Petukhov, A., Stokolos, A., Wick, B. (eds) Recent Advances in Harmonic Analysis and Applications. Springer Proceedings in Mathematics & Statistics, vol 25. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4565-4_30
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DOI: https://doi.org/10.1007/978-1-4614-4565-4_30
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