Fig. 1. Reconstruction results over the sparse_value. The numerical values on x-axis denote the sparse_value of signals and those on y-axis represent the SNR (a) and run time (b).
Fig. 7. The electrocardiography (ECG) signals in signal channel no#1 of three patients which are selected randomly from the PTB Diagnostic ECG Database: (a) the original signals , (b) with orthogonal Daubechies waveles (db1), (c)
Fig. 3. Reconstruction results over the sparse_value. The numerical values on x-axis denote the sparse_ value and those on y-axis represent the SNR (a) and run time (b).
Fig. 4. Reconstruction results over the number of block d. The numerical values on x-axis denote the number of block d and those on y-axis represent the SNR (a) and run time (b).
Fig. 5. Reconstruction results with unknown block d. The numerical values on x-axis denote the number of block d and those on y-axis represent the SNR (a) and run time (b); when we generate the source with block size d = 8.
Fig. 2. Reconstruction results over the number of measurement M. The numerical values on x-axis denote the number of measurement M and those on y-axis represent the SNR (a) and run time (b).
Fig. 6. Reconstruction results with unknown block d. The numerical values on x-axis denote the number of block d and those on y-axis represent the SNR (a) and run time (b); when we generate the source with block size d = 5.
Table 1. Average reconstruction SNR and run time of block sparse signals using different methods
References
- Q. Wang and Z. Liu, "A robust and efficient algorithm for distributed compressed sensing," Computers & Electrical Engineering, vol. 37, no. 6, pp. 916-926, 2011. https://doi.org/10.1016/j.compeleceng.2011.09.008
- H. Palangi, R. Ward, and L. Deng, "Convolutional deep stacking networks for distributed compressive sensing," Signal Processing, vol. 131, pp. 181-189, 2017. https://doi.org/10.1016/j.sigpro.2016.07.006
- Y. Oktar and M. Turkan, "A review of sparsity-based clustering methods," Signal Processing, vol. 148, pp. 20-30, 2018. https://doi.org/10.1016/j.sigpro.2018.02.010
- L. Vidya, V. Vivekanand, U. Shyamkumar, and M. Deepak, "RBF network based sparse signal recovery algorithm for compressed sensing reconstruction," Neural Networks, vol. 63, pp. 66-78, 2015. https://doi.org/10.1016/j.neunet.2014.10.010
- X. Li, H. Bai, and B. Hou, "A gradient-based approach to optimization of compressed sensing systems," Signal Processing, vol. 139, pp. 49-61, 2017. https://doi.org/10.1016/j.sigpro.2017.04.005
- G. Coluccia, A. Roumy, and E. Magli, "Operational rate-distortion performance of single-source and distributed compressed sensing," IEEE Transactions on Communications, vol. 62, no. 6, pp. 2022-2033, 2014. https://doi.org/10.1109/TCOMM.2014.2316176
- D. Baron, M. F. Duarte, M. B. Wakin, S. Sarvotham, and R. G. Baraniuk, "Distributed compressed sensing," 2009 [Online]. Available: https://arxiv.org/abs/0901.3403.
- Y. J. Zhang, R. Qi, and Y. Zeng, "Backtracking-based matching pursuit method for distributed compressed sensing," Multimedia Tools and Applications, vol. 76, no. 13, pp. 14691-14710, 2017. https://doi.org/10.1007/s11042-016-3933-x
- Y. Zhang, R. Qi, and Y. Zeng, "Forward-backward pursuit method for distributed compressed sensing," Multimedia Tools and Applications, vol. 76, no. 20, pp. 20587-20608, 2017. https://doi.org/10.1007/s11042-016-3968-z
- Y. C. Eldar and H. Rauhut, "Average case analysis of multichannel sparse recovery using convex relaxation," IEEE Transactions on Information Theory, vol. 56, no. 1, pp. 505-519, 2010. https://doi.org/10.1109/TIT.2009.2034789
- D. L. Donoho, "For most large underdetermined systems of linear equations the minimal l1-norm solution is also the sparsest solution," Communications on Pure and Applied Mathematics, vol. 59, no. 6, pp. 797-829, 2006. https://doi.org/10.1002/cpa.20132
- M. F. Duarte, S. Sarvotham, D. Baron, M. B. Wakin, and R. G. Baraniuk, "Distributed compressed sensing of jointly sparse signals," in Proceeding of the 39th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, 2005, pp. 1537-1541.
- M. B. Wakin, M. F. Duarte, S. Sarvotham, D. Baron, and R. G. Baraniuk, "Recovery of jointly sparse signals from few random projections," Advances in Neural Information Processing Systems, vol. 18, pp. 1435-1440, 2005.
- J. A. Tropp, A. C. Gilbert, and M. Strauss, "Simultaneous sparse approximation via greedy pursuit," in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing, Philadelphia, PA, 2005.
- D. Sundman, S. Chatterjee, and M. Skoglund, "Greedy pursuits for compressed sensing of jointly sparse signals," in Proceedings of 2011 19th European Signal Processing Conference, Barcelona, Spain, 2011, pp. 368-372.
- K. Lee, Y. Bresler, and M. Junge, "Subspace methods for joint sparse recovery," IEEE Transactions on Information Theory, vol. 58, no. 6, pp. 3613-3641, 2012. https://doi.org/10.1109/TIT.2012.2189196
- X. T. Yuan, X. Liu, and S. Yan, "Visual classification with multitask joint sparse representation," IEEE Transactions on Image Processing, vol. 21, no. 10, pp. 4349-4360, 2012. https://doi.org/10.1109/TIP.2012.2205006
- F. Parvaresh, H. Vikalo, S. Misra, and B. Hassibi, "Recovering sparse signals using sparse measurement matrices in compressed DNA microarrays," IEEE Journal of Selected Topics in Signal Processing, vol. 2, no. 3, pp. 275-285, 2008. https://doi.org/10.1109/JSTSP.2008.924384
- S. F. Cotter and B. D. Rao, "Sparse channel estimation via matching pursuit with application to equalization," IEEE Transactions of Communications, vol. 50, no. 3, pp. 374-377, 2002. https://doi.org/10.1109/26.990897
- R. Qi, D. Yang, Y. Zhang, and H. Li, "On recovery of block sparse signals via block generalized orthogonal matching pursuit," Signal Processing, vol. 153, pp. 34-46, 2018. https://doi.org/10.1016/j.sigpro.2018.06.023
- R. G. Baraniuk, V. Cevher, M. F. Duarte, and C. Hegde, "Model-based compressive sensing," IEEE Transactions on Information Theory, vol. 56, no. 4, pp. 1982-2001, 2010. https://doi.org/10.1109/TIT.2010.2040894
- D. Needell and J. A. Tropp, "CoSaMP: iterative signal recovery from incomplete and inaccurate samples," Applied and Computational Harmonic Analysis, vol. 26, no. 3, pp. 301-321, 2009. https://doi.org/10.1016/j.acha.2008.07.002
- Y. C. Eldar, P. Kuppinger, and H. Bolcskei, "Block-sparse signals: Uncertainty relations and efficient recovery," IEEE Transactions on Signal Processing, vol. 58, no. 6, pp. 3042-3054, 2010. https://doi.org/10.1109/TSP.2010.2044837
- L. Zelnik-Manor, K. Rosenblum, and Y. C. Eldar, "Dictionary optimization for block-sparse representations," IEEE Transactions on Signal Processing, vol. 60, no. 5, pp. 2386-2395, 2012. https://doi.org/10.1109/TSP.2012.2187642
- A. Kamali, M. A. Sahaf, A. D. Hooseini, and A. A. Tadaion, "Block subspace pursuit for block-sparse signal reconstruction," Iranian Journal of Science and Technology: Transactions of Electrical Engineering, vol. 37, no. E1, pp. 1-16, 2013.
- B. X. Huang and T. Zhou, "Recovery of block sparse signals by a block version of StOMP," Signal Processing, vol. 106, pp. 231-244, 2015. https://doi.org/10.1016/j.sigpro.2014.07.023
- R. Qi, Y. Zhang, and H. Li, "Block sparse signals recovery via block backtracking-based matching pursuit method," Journal of Information Processing Systems, vol. 13, no. 2, pp. 360-369, 2017. https://doi.org/10.3745/JIPS.04.0030
- E. Candes, J. Romberg, and T. Tao, "Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information," IEEE Transactions on Information Theory, vol. 52, no. 2, pp. 489-509, 2006. https://doi.org/10.1109/TIT.2005.862083
- A. L. Goldberger, L. A. Amaral, L. Glass, J. M. Hausdorff, P. C. Ivanov, R. G. Mark, J. E. Mietus, G. B. Moody, C. K. Peng, and H. E. Stanley, "PhysioBank, PhysioToolkit, and PhysioNet: components of a new research resource for complex physiologic signals," Circulation, vol. 101, no. 23, pp. e215-e220, 2000.