Design and realization of random measurement scheme for compressed sensing

Cheng-jun Xie; Lin Xu

doi:10.1007/s11801-012-1097-0

Optoelectronics Letters ›› 2012, Vol. 8 ›› Issue (1) : 60-62. DOI: 10.1007/s11801-012-1097-0

Article

Design and realization of random measurement scheme for compressed sensing

Cheng-jun Xie¹^,^a ,
Lin Xu¹

Author information +

History +

Abstract

Design and realization of random measurement scheme for compressed sensing (CS) are presented in this paper, and lower limits of the measurement number are achieved when the precise reconstruction is realized. Four kinds of random measurement matrices are designed according to the constraint conditions of random measurement. The performance is tested employing the algorithm of stagewise orthogonal matching pursuit (StOMP). Results of the experiment show that lower limits of the measurement number are much better than the results described in Refs.[13–15]. When the ratios of measurement to sparsity are 3.8 and 4.0, the mean relative errors of the reconstructed signals are 8.57 × 10⁻¹³ and 2.43 × 10⁻¹⁴, respectively, which confirms that the random measurement scheme of this paper is very effective.

Keywords

Compress Sense / Synthetic Aperture Radar / Random Measurement / Measurement Matrix / Compress Sense Theory

Cite this article

EndNote

Ris (Procite)

Bibtex

Download citation ▾

Cheng-jun Xie, Lin Xu. Design and realization of random measurement scheme for compressed sensing. Optoelectronics Letters, 2012, 8(1): 60‒62 https://doi.org/10.1007/s11801-012-1097-0

References

Publishing order | Descend order by publishing year | Descend order by cited within

[1]	DonohoD.. IEEE Transactions on Information Theory, 2006, 52: 1289 CrossRef Google scholar

[2]	CandèsE., RombergJ., TaoT.. IEEE Transactions on Information Theory, 2006, 52: 489 CrossRef Google scholar

[3]	RombergJ.. IEEE Signal Processing Magazine, 2006, 25: 14 CrossRef Google scholar

[4]	DuarteM. F., DavenportM. A., TakharD., SunT., KellyK. F., BaraniukR. G.. IEEE Signal Processing Magazine, 2008, 25: 83 CrossRef Google scholar

[5]	Baraniuk R and Steeghs P, Compressive Radar Imaging, IEEE: Proceedings of the Radar Conference, Washington D.C., 128 (2007).

[6]	Bhattacharya S, Blumensath T, Mulagrew B and Davies M, Fast Encoding of Synthetic Aperture Radar Raw Data Using Compressed Sensing, IEEE Proceedings of Statistical Signal Processing, Washington D. C., 448 (2007).

[7]	LustigM., DonohoD. L., PaulyJ. M.. Magnetic Resonance in Medicine, 2007, 58: 1182 CrossRef Google scholar

[8]	HuS., LustigM., ChenA. P., CraneJ., KerrA., KelleyD. A., HurdR., KurhanewiczJ., NelsonS. J., PaulyJ. M., VigneronD. B.. Journal of Magnetic Resonance, 2008, 192: 258 CrossRef Google scholar

[9]	CandèsE., TaoT.. IEEE Transaction on Information Theory, 2005, 51: 4203 CrossRef Google scholar

[10]	CandèsE., RombergJ.. Found. Comput. Math., 2006, 6: 227 CrossRef Google scholar

[11]	CandèsE., WakinM. B.. IEEE Signal Processing Magazine, 2008, 25: 21 CrossRef Google scholar

[12]	Gemmeke J F and Cranen B, Using Sparse Representations for Missing Data Imputation in Noise Robust Speech Recognition, European Signal Processing Conf. (EUSIPCO), Lausanne, Switzerland, 987 (2008).

[13]	BaraniukR.. IEEE Signal Processing Magazing, 2007, 24: 118 CrossRef Google scholar

[14]	ShiG.-m., LiuD.-h., GaoD.-h., LiuZ., LinJ., WangL.-j.. Acta Electronica Sinica, 2009, 37: 1070

[15]	GaoR.. Matching Pursuit Algorithm for Image Reconstruction Based on Compressive Sensing, 2009, Beijing, Beijing Jiaotong University: 2

This work has been supported by the National Natural Science Foundation of China (Nos.61072111 and 60672156), and the Project of Science and Technology Commission of Jilin Province (Nos.20100503 and 20110360).