Abstract
In this paper we propose an approach for underdetermined blind separation in the case of additive Gaussian white noise and pink noise in addition to the most challenging case where the number of source signals is unknown. In addition to that, the proposed approach is applicable in the case of separating I + 3 source signals from I mixtures with an unknown number of source signals and the mixtures have additive two kinds of noises. This situation is more challenging and also more suitable to practical real world problems. Moreover, unlike to some traditional approaches, the sparsity conditions are not imposed. Firstly, the number of source signals is approximated and estimated using multiple source detection, followed by an algorithm for estimating the mixing matrix based on combining short time Fourier transform and rough-fuzzy clustering. Then, the mixed signals are normalized and the source signals are recovered using multi-layer modified Gradient descent Local Hierarchical Alternating Least Squares Algorithm exploiting the number of source signals estimated , and the mixing matrix obtained as an input and initialized by multiplicative algorithm for matrix factorization based on alpha divergence. The computer simulation results show that the proposed approach can separate I + 3 source signals from I mixed signals, and it has superior evaluation performance compared to some traditional approaches in recent references.
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References
Alshabrawy, O.S., Ghoniem, M.E., Awad, W.A., Hassanien, A.E.: Underdetermined Blind Source Separation based on Fuzzy C-Means and Semi-Nonnegative Matrix Factorization. In: IEEE Federated Conference on Computer Science and Iinformation Systems (FedCSIS), Wroclaw, Poland, September 9-12, pp. 695–700 (2012)
Yadong, L., Zongtan, Z., Dewen, H.: A novel method for spatio temporal pattern analysis of brain fMRI data. Science in China Series F: Information Sciences 48(2), 151–160 (2005)
Araki, S., Makino, S., Sawada, H., Mukai, R.: Underdetermined blind separation of convolutive mixtures of speech with directivity pattern based mask and ICA. In: Puntonet, C.G., Prieto, A.G. (eds.) ICA 2004. LNCS, vol. 3195, pp. 898–905. Springer, Heidelberg (2004)
Ohnishi, N., Imiya, A.: Independent component analysis of optical flow for robot navigation. Neurocomputing 7(10-12), 2140–2163 (2008)
Tonazzini, A., Bedini, L., Salerno, E.: A Markov model for blind image separation by a mean-field EM algorithm. IEEE Transactions on Image Processing 15(2), 473–482 (2005)
Er-Wei, B., QingYu, L., Zhiyong, Z.: Blind source separation channel equalization of nonlinear channels with binary inputs. IEEE Transactions on Signal Processing 53(7), 2315–2323 (2005)
Peng, D., Xiang, Y.: Underdetermined blind separation of nonsparse sources using spatial time-frequency distributions. Digital Signal Processing 20, 581–596 (2010)
Lu, F., Huang, Z., Jiang, W.: Underdetermined blind separation of non-disjoint signals in time frequency domain based on matrix diagonalization. Signal Processing 91, 1568–1577 (2011)
Kim, S., Yoo, C.D.: Underdetermined Blind Source Separation Based on Subspace Representation. IEEE Transaction on Signal Processing 57(7) (July 2009)
Cichocki, A., Phan, A.H., Caiafa, C.: FlexibleHALSalgorithms for sparse non-negative matrix/tensor factorization. In: Proc. of 18th IEEE Workshops on Machine Learning for Signal Processing, Cancun, Mexico, pp. 16–19 (2008)
Cichocki, A., Zdunek, R., Amari, S.-i.: Hierarchical ALS algorithms for nonnegative matrix and 3-D tensor factorization. In: Davies, M.E., James, C.J., Abdallah, S.A., Plumbley, M.D. (eds.) ICA 2007. LNCS, vol. 4666, pp. 169–176. Springer, Heidelberg (2007)
Cichocki, A., Zdunek, R., Phan, A.H., Amari, S.-I.: Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation. John Wiley (2009)
Snoussi, H., Idier, J.: Bayesian blind separation of generalized hyperbolic processes in noisy and underdeterminate mixtures. IEEE Transactions on Signal Processing 54(9), 3257–3269 (2006)
Peng, D., Xiang, Y.: Underdetermined blind separation of non-sparse sources using spatial time-frequency distributions. Digital Signal Processing 20, 581–596 (2010)
Sun, S., Peng, C., Hou, W., Zheng, J., Jiang, Y., Zheng, X.: Blind source separation with time series variational Bayes expectation maximization algorithm. Digital Signal Processing 22, 17–33 (2012)
Sun, H., Wang, S., Jiang, Q.: FCM-based model selection algorithms for determining the number of clusters. Pattern Recognition 37(10), 2027–2037 (2004)
Cichocki, A., Zdunek, R.: Multilayer nonnegative matrix factorization. Electronics Letters 42(16), 947–948 (2006)
Cichocki, A., Zdunek, R.: Multilayer nonnegative matrix factorization using projected gradient approaches. In: The 13th International Conference on Neural Information Processing (ICONIP 2006), Hong Kong, October 3-6 (2006)
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Alshabrawy, O.S., Hassanien, A.E. (2014). Underdetermined Blind Separation of Mixtures of an Unknown Number of Sources with Additive White and Pink Noises. In: Kömer, P., Abraham, A., Snášel, V. (eds) Proceedings of the Fifth International Conference on Innovations in Bio-Inspired Computing and Applications IBICA 2014. Advances in Intelligent Systems and Computing, vol 303. Springer, Cham. https://doi.org/10.1007/978-3-319-08156-4_24
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DOI: https://doi.org/10.1007/978-3-319-08156-4_24
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08155-7
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