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An adaptive compressed sensing architecture based on selective measure is proposed in this paper, in order to reduce the effects of non-sparse noise component on the performance of existing compressed sensing reconstruction algorithm. Firstly, in this paper we analyze and deduces the statistics characteristic of the measured noise and its influence on the reconstruction performance; then we propose a compressive-domain projection filter combined with iterative noise detector method to obtain the location information of noise subspace based on minimal output energy criteria; thirdly, we measure matrix adaptively with the location information, and focus on the signal subspace directly without sensing the noise component in analog part. Simulation results show that compared with the existing compressed sensing procedures, our method can obviously improve the performance of reconstruction of signals with noise, and can be used to perform the front-end spectrum analysis of absorbing materials and better detect the active channels in cognitive radio.
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Keywords:
- spectrum sensing /
- compressed sensing /
- signal reconstruction /
- selective measure
[1] Sun L K, Cheng H F, Zhou Y J, Wang J 2012 Chin. Phys. B 21 055201
[2] Zhou Y J, Pang Y Q, Cheng H F 2013 Chin. Phys. B 22 015201
[3] Donoho D L 2006 IEEE Trans. Inform. Theory 52 1289
[4] Candes E J 2006 Proceedings of the International Congress of Mathematicians Madrid, Spain, August 22-30, 2006 p1433
[5] Candes E J, Romberg J, Tao T 2006 IEEE Trans. Inform. Theory 52 489
[6] Zhang J C, Fu N, Qiao L Y, Peng X Y 2014 Acta Phys. Sin. 63 030701 (in Chinese) [张京超, 付宁, 乔立岩, 彭喜元 2014 63 030701]
[7] Sun B, Jiang J J 2011 Acta Phys. Sin. 60 110701 (in Chinese) [孙彪, 江建军 2011 60 110701]
[8] Donoho D L, Tsaig Y 2006 Signal Process. 86 533
[9] Tibshirani R 1996 J. Roy. Stat. Soc. B 58 267
[10] Figueiredo M A T, Nowak R D, Wright S J 2007 IEEE J. Sel. Top. Sig. Proc. 1 586
[11] Gorodnitsky I F, Rao B D 1997 IEEE Trans. Sig. Proc. 45 600
[12] Rao B D, Engan K, Cotter S F 2003 IEEE Trans. Sig. Proc. 51 760
[13] Neff R, Zakhor A 1997 IEEE Trans. Circ. Syst. Vide. 7 158
[14] Needell D, Vershynin R 2010 IEEE Trans. Sel. Top. Sig. Proc. 4 310
[15] Donoho D L, Tsaig Y, Drori I 2012 IEEE Trans. Inform. Theory. 58 1094
[16] Davenport M A, Wakin M B 2010 IEEE Trans. Inform. Theory 56 4395
[17] Tropp J A, Gilbert A C 2007 IEEE Trans. Inform. Theory 53 4655
[18] Varadarajan B, Khudanpur S, Trac T D 2011 IEEE Sig. Proc. Lett. 18 27
[19] Haupt J, Castro R M, Nowak R 2011 IEEE Trans. Inform. Theory 57 6222
[20] Davenport M A, Arias-Castro E 2012 Proceedings of the IEEE International Symposium on Information Theory Massachusetts Ave, USA, July 1-6, 2012 p1827
[21] Hanneke S 2011 Ann. Stat. 39 333
[22] Koltchinskii V 2010 J. Mach. Learn. Res. 11 2457
[23] Laska J N, Kirolos S, Duarte M F 2007 Proceedings of the IEEE International Symposium on Circuits and Systems New Orleans, Louisiana, USA, May 27-30, 2007 p1959
[24] Baraniuk R 2007 IEEE Sig. Proc. Mag. 24 118
[25] Donoho D L 2006 Commun. Pur. Appl. Math. 59 797
[26] Eldar Y C, Kuppinger P, Bolcskei H 2010 IEEE Trans. Sig. Proc. 58 3042
[27] Daubechies I, Devore R, Fornasier M, Gunturk C S 2010 Comm. Pure Appl. Math. 63 1
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[1] Sun L K, Cheng H F, Zhou Y J, Wang J 2012 Chin. Phys. B 21 055201
[2] Zhou Y J, Pang Y Q, Cheng H F 2013 Chin. Phys. B 22 015201
[3] Donoho D L 2006 IEEE Trans. Inform. Theory 52 1289
[4] Candes E J 2006 Proceedings of the International Congress of Mathematicians Madrid, Spain, August 22-30, 2006 p1433
[5] Candes E J, Romberg J, Tao T 2006 IEEE Trans. Inform. Theory 52 489
[6] Zhang J C, Fu N, Qiao L Y, Peng X Y 2014 Acta Phys. Sin. 63 030701 (in Chinese) [张京超, 付宁, 乔立岩, 彭喜元 2014 63 030701]
[7] Sun B, Jiang J J 2011 Acta Phys. Sin. 60 110701 (in Chinese) [孙彪, 江建军 2011 60 110701]
[8] Donoho D L, Tsaig Y 2006 Signal Process. 86 533
[9] Tibshirani R 1996 J. Roy. Stat. Soc. B 58 267
[10] Figueiredo M A T, Nowak R D, Wright S J 2007 IEEE J. Sel. Top. Sig. Proc. 1 586
[11] Gorodnitsky I F, Rao B D 1997 IEEE Trans. Sig. Proc. 45 600
[12] Rao B D, Engan K, Cotter S F 2003 IEEE Trans. Sig. Proc. 51 760
[13] Neff R, Zakhor A 1997 IEEE Trans. Circ. Syst. Vide. 7 158
[14] Needell D, Vershynin R 2010 IEEE Trans. Sel. Top. Sig. Proc. 4 310
[15] Donoho D L, Tsaig Y, Drori I 2012 IEEE Trans. Inform. Theory. 58 1094
[16] Davenport M A, Wakin M B 2010 IEEE Trans. Inform. Theory 56 4395
[17] Tropp J A, Gilbert A C 2007 IEEE Trans. Inform. Theory 53 4655
[18] Varadarajan B, Khudanpur S, Trac T D 2011 IEEE Sig. Proc. Lett. 18 27
[19] Haupt J, Castro R M, Nowak R 2011 IEEE Trans. Inform. Theory 57 6222
[20] Davenport M A, Arias-Castro E 2012 Proceedings of the IEEE International Symposium on Information Theory Massachusetts Ave, USA, July 1-6, 2012 p1827
[21] Hanneke S 2011 Ann. Stat. 39 333
[22] Koltchinskii V 2010 J. Mach. Learn. Res. 11 2457
[23] Laska J N, Kirolos S, Duarte M F 2007 Proceedings of the IEEE International Symposium on Circuits and Systems New Orleans, Louisiana, USA, May 27-30, 2007 p1959
[24] Baraniuk R 2007 IEEE Sig. Proc. Mag. 24 118
[25] Donoho D L 2006 Commun. Pur. Appl. Math. 59 797
[26] Eldar Y C, Kuppinger P, Bolcskei H 2010 IEEE Trans. Sig. Proc. 58 3042
[27] Daubechies I, Devore R, Fornasier M, Gunturk C S 2010 Comm. Pure Appl. Math. 63 1
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