Iterative method for simultaneous sparse approximation

Document Type : Article


1 Advanced Communication Research Institute (ACRI), Electrical Engineering Department, Sharif University of Technology, Tehran,Iran.

2 Advanced Communication Research Institute (ACRI), Electrical Engineering Department, Sharif University of Technology, Tehran, Iran.


This paper studies the problem of Simultaneous Sparse Approximation (SSA). This problem arises in many applications which work with multiple signals maintaining some degree of dependency such as radar and sensor networks. In this paper, we introduce a new method towards joint recovery of several independent sparse signals with the same support. We provide an analytical discussion on the convergence of our method called Simultaneous Iterative Method (SIM). Additionally, we compare our method with other group-sparse reconstruction techniques, i.e., Simultaneous Orthogonal Matching Pursuit (SOMP), and Block Iterative Method with Adaptive Thresholding (BIMAT) through numerical experiments. The simulation results demonstrate that SIM outperforms these algorithms in terms of the metrics Signal to Noise Ratio (SNR) and Success Rate (SR). Moreover, SIM is considerably less complicated than BIMAT, which makes it feasible for practical applications such as implementation in MIMO radar systems.


Main Subjects

1. Cand_es, E.J., Romberg, J., and Tao, T. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information", IEEE Trans. of Inf. Theory, 52(2), pp. 489-509 (2006). 2. Donoho, D.L. Compressed sensing", IEEE Trans. of Inf. Theory, 52(4), pp. 1289-1306 (2006). 3. Abbasi, H., Kavehvash, Z., and Shabany, M. Improved CT image reconstruction through partial Fourier sampling", Sci. Iran., 23(6), pp. 2908-2916 (2016). 4. Amezquita-Sanchez, J. and Adeli, H. Feature extraction and classi_cation techniques for health monitoring of structures", Sci. Iran. A, Civ. Eng., 22(6), p. 1931 (2015). 5. Duarte, M.F., Cevher, V., and Baraniuk, R.G. Model-based compressive sensing for signal ensembles", 47th Annu. Allerton Conf. on Commun., Control, and Comput., IEEE, pp. 244-250 (2009). 6. Gastpar, M. and Vetterli, M. Source-channel communication in sensor networks", IPSN, Springer, pp. 162- 177 (2003). 7. Gorodnitsky, I.F., George, J.S., and. Rao, B.D. Neuromagnetic source imaging with focuss: a recursive weighted minimum norm algorithm", Electroencephalogr. and Clin. Neurophysiol., 95(4), pp. 231-251 (1995). 8. Malioutov, D., Cetin M., and Willsky, A.S. A sparse signal reconstruction perspective for source localization with sensor arrays", IEEE Trans. on Signal Process., 53(8), pp. 3010-3022 (2005). 9. Ibernon-Fernandez, R., Molina-Garcia-Pardo, J.M., and Juan-Llacer, L. Comparison between measurements and simulations of conventional and distributed mimo system", IEEE Antennas and Wirel. Propag. Lett., 7, pp. 546-549 (2008). 10. Mohammadi, E., Fallah, A., and Marvasti, F. Sampling and distortion tradeo_s for indirect source retrieval", IEEE Trans. on Inf. Theory, 63(11), pp. 6833-6848 (2017). 11. Tropp, J.A. and Gilbert, A.C. Signal recovery from random measurements via orthogonal matching pursuit", IEEE Trans, on Inf. Theory, 53(12), pp. 4655- 4666 (2007). 12. Determe, J.F., Louveaux, J., Jacques, L., and Horlin, F. On the noise robustness of simultaneous orthogonal matching pursuit", IEEE Trans. on Signal Process., 65(4), pp. 864-875 (2017). 13. Tropp, J.A., Gilbert, A.C., and Strauss, M.J. Algorithms for simultaneous sparse approximation. part i: Greedy pursuit", Signal Process., 86(3), pp. 572-588 (2006). 14. Rakotomamonjy, A. Surveying and comparing simultaneous sparse approximation (or group-lasso) algorithms", Signal Process., 91(7), pp. 1505-1526 (2011). 15. Marvasti, F., Azghani, M., Imani, P., Pakrouh, P., Heydari, S.J., Golmohammadi, A., Kazerouni, A., and Khalili, M. Sparse signal processing using iterative method with adaptive thresholding (IMAT)", 19th Int. Conf. on Telecommun. (ICT), IEEE, pp. 1-6 (2012). 16. Marvasti, F., Amini, A., Haddadi, F., Soltanolkotabi, M., Khalaj, B.H., Aldroubi, A., Sanei, S., and Chambers, J. A uni_ed approach to sparse signal processing", EURASIP J. on Adv. in Signal Process., 2012(1), p. 44 (2012). 17. Marvasti, F., Nonuniform sampling: theory and practice, Springer Science & Business Media (2012). 18. Marvasti, F. and Mashadi, M.B. Wideband analog to digital conversion by random or level crossing sampling", U.S. Patent 9,729,160 (2017). 19. Zarmehi, N. and Marvasti, F. Sparse and low-rank recovery using adaptive thresholding", Digit. Signal Process., 73, pp. 145-152 (2018). 20. Azghani, M., Ghorbani A., and Marvasti, F. Blind iterative nonlinear distortion compensation based on thresholding", IEEE Trans. on Circuits and Syst. II: Express Briefs, 64(7), pp. 852-856 (2017). 21. Mashhadi, M.B., Salarieh, N., Farahani, E.S., and Marvasti, F. Level crossing speech sampling and its sparsity promoting reconstruction using an iterative method with adaptive thresholding", IET Signal Process., 11(6), pp. 721-726 (2017). 22. Abtahi, A., Azghani, M., Taye_, J., and Marvasti, F. Iterative block-sparse recovery method for distributed mimo radar", in Iran Workshop on Commun. and Inf. Theory (IWCIT), IEEE, pp. 1-4 (2016). 23. Zayyani, H., Babaie-Zadeh, M., and Jutten, C. An iterative Bayesian algorithm for sparse component analysis in presence of noise", IEEE Trans. on Signal Process., 57(11), pp. 4378-4390 (2009). 24. Esmaeili, A., Kangarshahi, E.A., and Marvasti, F. Iterative null space projection method with adaptive thresholding in sparse signal recovery", IET Signal Process, 12(5), pp. 605-612 (2018).