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
Donoho, D.: Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006)
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)
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)
Zhang, T.: Sparse recovery with orthogonal matching pursuit under RIP. IEEE Trans. Inf. Theory 57(9), 6215–6221 (2011)
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)
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)
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
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
Peyré, G.: Manifold models for signals and images. Comput. Vis. Image Underst. 113(2), 249–260 (2009)
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)
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)
Baraniuk, R., Wakin, M.: Random projections of smooth manifolds. Found. Comput. Math. 9(1), 51–77 (2009)
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)
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)
Scholz, M., Kaplan, F., Guy, C.L., Kopka, J., Selbig, J.: Non-linear PCA: a missing data approach. Bioinformatics 21(20), 3887–3895 (2005)
Mairal, J., Bach, F., Ponce, J., Sapiro, G.: Online learning for matrix factorization and sparse coding. J. Mach. Learn. Res. 11, 19–60 (2010)
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)
SPAMS: Sparse modeling software (2014). http://spams-devel.gforge.inria.fr/
Koh, K., Kim, S., Boyd, S.: l1 ls: A Matlab Solver for Large-scale l1-Regularized Least Squares Problems. Stanford University, Stanford (2007)
Tenenbaum, J., Silva, V., Langford, J.: A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323 (2000)
Hinton, G., Dayan, P., Revow, M.: Modeling the manifolds of images of handwritten digits. IEEE Trans. Neural Netw. 8(1), 65–74 (1997)
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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