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A novel dictionary-based approach for missing sample recovery of signals in manifold

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Abstract

Recovery of signal with randomly positioned missing samples is a difficult or impossible task. The aim of this paper is to accurately recover missing samples if prior information on domain of sparsity is known. This paper proposes a novel approach for recovery of signals lying in low-dimensional sub-manifold, embedded in high-dimensional signal space and heavily corrupted by arbitrarily positioned missing samples. The proposed simple and efficient algorithm is based on global manifold model and can recover the corrupted signal from the limited available samples without affecting the remaining samples. The proposed method is applicable to any type of data and can be extensively used in a wide variety of data processing techniques. Experimental results prove that the proposed method outperforms the counterparts without much computational complexity.

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References

  1. Donoho, D.: Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  2. Huper, K., Trumpf, J.: Newton-like methods for numerical optimization on manifolds. In: Conference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers, vol. 1, pp. 136–139 (2004)

  3. Stankovic, L., Dakovic, M., Vujovic, S.: Adaptive variable step algorithm for missing samples recovery in sparse signals. IET Signal Process. 8(3), 246–256 (2014)

    Article  Google Scholar 

  4. Zhang, T.: Sparse recovery with orthogonal matching pursuit under RIP. IEEE Trans. Inf. Theory 57(9), 6215–6221 (2011)

    Article  MathSciNet  Google Scholar 

  5. Stankovic, L., Stankovic, S., Amin, M.: Missing samples analysis in signals for applications to L-estimation and compressive sensing. Signal Process. 94, 401–408 (2014)

    Article  Google Scholar 

  6. Shah, P., Chandrasekaran, V.: Iterative projections for signal identification on manifolds: global recovery guarantees. In: 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton), pp. 760–767 (2011)

  7. Greeshma, N.K., Baburaj, M., George, Sudhish N.: Reconstruction of cloud-contaminated satellite remote sensing images using kernel PCA-based image modelling. Arab. J. Geosci. 9(3), 1–14 (2016). doi:10.1007/s12517-015-2199-3

    Google Scholar 

  8. Carreira-Perpinan, M., Lu, Z.: Manifold learning and missing data recovery through unsupervised regression. In: 2011 IEEE 11th International Conference on Data Mining (ICDM), pp. 1014–1019 (2011). doi:10.1109/ICDM.2011.97

  9. Peyré, G.: Manifold models for signals and images. Comput. Vis. Image Underst. 113(2), 249–260 (2009)

  10. Aharon, M., Elad, M., Bruckstein, A.: K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans. Signal Process. 54(11), 4311–4322 (2006)

    Article  Google Scholar 

  11. Chen, M., Silva, J., Paisley, J., Wang, C., Dunson, D., Carin, L.: Compressive sensing on manifolds using a nonparametric mixture of factor analyzers algorithm and performance bounds. IEEE Trans. Signal Process. 59(3), 1329–1329 (2011)

  12. Baraniuk, R., Wakin, M.: Random projections of smooth manifolds. Found. Comput. Math. 9(1), 51–77 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  13. Hegde, C., Baraniuk, R.: Spin: iterative signal recovery on incoherent manifolds. In: 2012 IEEE International Symposium on Information Theory Proceedings (ISIT), pp. 1296–1300 (2012)

  14. Wakin, M., Baraniuk, R.: Random projections of signal manifolds. In: 2006 IEEE International Conference on Acoustics, Speech and Signal Processing. ICASSP 2006 Proceedings, vol. 5, p. V (2006)

  15. Scholz, M., Kaplan, F., Guy, C.L., Kopka, J., Selbig, J.: Non-linear PCA: a missing data approach. Bioinformatics 21(20), 3887–3895 (2005)

    Article  Google Scholar 

  16. Mairal, J., Bach, F., Ponce, J., Sapiro, G.: Online learning for matrix factorization and sparse coding. J. Mach. Learn. Res. 11, 19–60 (2010)

    MathSciNet  MATH  Google Scholar 

  17. Yang, J., Yuan, X., Liao, X., Llull, P., Brady, D., Sapiro, G., Carin, L.: Video compressive sensing using gaussian mixture models. IEEE Trans. Image Process. 23(11), 4863–4878 (2014)

    Article  MathSciNet  Google Scholar 

  18. SPAMS: Sparse modeling software (2014). http://spams-devel.gforge.inria.fr/

  19. Koh, K., Kim, S., Boyd, S.: l1 ls: A Matlab Solver for Large-scale l1-Regularized Least Squares Problems. Stanford University, Stanford (2007)

    Google Scholar 

  20. Tenenbaum, J., Silva, V., Langford, J.: A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323 (2000)

    Article  Google Scholar 

  21. Hinton, G., Dayan, P., Revow, M.: Modeling the manifolds of images of handwritten digits. IEEE Trans. Neural Netw. 8(1), 65–74 (1997)

    Article  Google Scholar 

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Correspondence to Baburaj Madathil.

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Madathil, B., George, S.N. A novel dictionary-based approach for missing sample recovery of signals in manifold. SIViP 11, 283–290 (2017). https://doi.org/10.1007/s11760-016-0934-1

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  • DOI: https://doi.org/10.1007/s11760-016-0934-1

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