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The mean shift method of chaotic sequences in the study of compressive sensing

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Abstract

This paper presents a novel reconstruction approach of digital image in compressive sensing by the use of mean shift of different chaotic sequence to the measurement matrix. This matrix preserves better details of the structures of the recovered images, and enables a systematic construction of the measurement matrices of it. This proposed approach provides not only visible Peak Signal to Noise Ratio improvements over state-of-the-art methods (e.g. the Gaussian random matrix method) but also better preservation of the image structures during compression, which in turn enables better visual quality in image recovery, as illustrated in our experimental results.

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References

  1. Cheng Y (1995) Mean shift, mode seeking, and clustering, Pattern Analysis and Machine Intelligence. IEEE Trans 17(8):790–799

  2. Yu-Ren L, Kuo-Liang C, Chyou-Hwa C, Guei-Yin L, Wang CH (2012) Novel mean-shift based histogram equalization using textured regions. Expert Syst Appl 39(3):2750–2758

  3. Estellers V, Thiran J-P, Bresson X (2013) Enhanced Compressed Sensing Recovery With Level Set Normals. IEEE Trans Image Process 22(7):2611–2626

    Article  Google Scholar 

  4. Guo W, Yin W (2010) Edge CS: Edge guided compressive sensing reconstruction, Proc SPIE Visual Commun Image Process 17–23

  5. Senoussaoui M , Kenny P, Stafylakis T, Dumouchel P (2014) A Study of the cosine distance-based mean shift for telephone speech diarization, audio, speech, and language processing. IEEE/ACM Trans 22(1):217–227

  6. Comaniciu D, Meer P (2002) Mean shift: a robust approach toward feature space analysis, Pattern Analysis and Machine Intelligence. IEEE Trans 24(5):603–619

  7. Mayer A, Greenspan H (2009) An adaptive mean-shift framework for MRI brain segmentation, medical imaging. IEEE Trans 28(8):1238–1250

  8. Candes E, Romberg J, Tao T (2006) Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inform Theory 52(2):489–509

    Article  MathSciNet  MATH  Google Scholar 

  9. Donoho D (2006) Compressed sensing. IEEE Trans Inform Theory 52(4):1289–1306

    Article  MathSciNet  MATH  Google Scholar 

  10. Lei Y, Barbot JP, Gang Z, Hong S (2010) Compressive sensing with chaotic sequence. IEEE Signal Process Lett 17(8):731–734

    Article  Google Scholar 

  11. Frunzete M, Lei Y, Barbot J, Vlad A (2011) Compressive sensing matrix designed by tent map, for secure data transmission,Signal Processing Algorithms,Architectures,Arrangements,and Applications Conference Proceedings pp 1–6

  12. Petras I (2011) Fractional-order nonlinear systems: modeling, analysis and simulation, Nonlinear Physical Science

  13. Yin W, Osher S, Darbon J, Goldfarb D (2008) Bregman iterative algorithms for compressed sensing and related problems. SIAM J Imaging Sci 1(1):143–168

    Article  MathSciNet  MATH  Google Scholar 

  14. Osher S, Mao Y, Dong B, Yin W (2010) Fast linearized bregman iteration for compressive sensing and sparse denoising. Commun Math Sci 8(1):93–111

    Article  MathSciNet  MATH  Google Scholar 

  15. Goldstein T, Osher S (2009) The split Bregman method for L1-regularized problems. SIAM J Imaging Sci 2(2):323–343

    Article  MathSciNet  MATH  Google Scholar 

  16. Cai JF, Osher S, Shen Z (2009) Linearized Bregman iterations for frame-based image deblurring. SIAM J Imaging Sci 2(1):226–252

    Article  MathSciNet  MATH  Google Scholar 

  17. Tropp JA, Gilbert AC (2007) Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit. IEEE Trans Inform Theory 53(12):4655–4666

    Article  MathSciNet  MATH  Google Scholar 

  18. Li P, Wang Q, Zuo W, Zhang L (2013) Log-euclidean kernels for sparse representation and dictionary learning, In ICCV

  19. Tian WB, Kang J, Zhang Y, Rui GS, Zhang HB (2014) Weakly matching pursuit denoising recovery for compressed sensing based on kalman filtering. ACTA Electr SINICA 42(6):1762–1767

    Google Scholar 

  20. Thrampoulidis C, Oymak S, Hassibi B (2015) Recovering structured signals in noise: least-squares meets compressed sensing, compressed sensing and its applications, Springer International Publishing, ISBN:978-3-319-16041-2

  21. Tan J, Ma YT, Baron D (2015) Compressive imaging via approximate message passing with image denoising. IEEE Transa Signal Process 63(8):424–428

    Article  MathSciNet  Google Scholar 

  22. Sermwuthisarn P, Gansawat D, Patanavijit V, Auethavekiat S (2015) Impulsive noise rejection method for compressed measurement signal in compressed sensing. EURASIP J Adv Signal Process pp 1–23

  23. Lim FL, West GA, Venkatesh S (1997) Use of log polar space for foveation and feature recognition. IEEE Proceed Vision Image Signal Process pp 323–331

  24. Ciocoiu IB (2011) Compressed sensing meets the human visual system. Springer Berlin Heidelberg, ISBN:978-3-642-24081-2

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Acknowledgments

This work is partially supported by National Natural Science Foundation of China (No. 61370186, No. 61473322), State Scholarship Fund (No. 2007104752), Researching Fund for Professors and Doctors (No. 2013ARF03) of Guangdong University of Education, Research personnel fostered by Guangdong Province in Thousand, Hundred and Ten, Science and Technology Planning Project of Guangdong Province (No. 2014A010103040, No. 2014B010116001, No. 2013A011403002), Science and Technology Planning Project of Guangzhou (No. 2014J4100032, No. 201510010203), Natural Science Foundation Project of Guangdong Province (No. 2015A030310194).

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Authors and Affiliations

  1. Department of Computer Science, Guangdong University of Education, Guangzhou, 510310, Guangdong, China

    Guoming Chen & Qiang Chen

  2. Department of Computer Science, JiNan University, Guangzhou, 510632, Guangdong, China

    Shun Long & Weiheng Zhu

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  1. Guoming Chen
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  2. Qiang Chen
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  3. Shun Long
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  4. Weiheng Zhu
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Correspondence to Guoming Chen.

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Chen, G., Chen, Q., Long, S. et al. The mean shift method of chaotic sequences in the study of compressive sensing. Int. J. Mach. Learn. & Cyber. 8, 1643–1654 (2017). https://doi.org/10.1007/s13042-016-0534-y

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  • DOI: https://doi.org/10.1007/s13042-016-0534-y

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