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Adaptive Hybrid Wavelet Regularization Method for Compressive Imaging

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Cloud Computing and Security (ICCCS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 10603))

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Abstract

This paper proposes a hybrid method that simultaneously considers sparsity in wavelet domain and image self-similarity by using wavelet L1 norm, nonlocal wavelet L0 norm regularization in image compressive sensing (CS) recovery. An auxiliary variable is then introduced to decompose this composite constraint problem into two simpler regularization sub-problems. Based on Fast Iterative Shrinkage-Thresholding Algorithm (FISTA), the sub-problems corresponding to the wavelet L1 norm and the nonlocal wavelet L0 norm are then solved by soft thresholding and adaptive hard thresholding respectively. The threshold of the later is decreased according to the energy of measurement error, leading to an adaptive hybrid regularization method. Experimental results show that it outperforms several excellent CS techniques.

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References

  1. Donoho, D.L.: Compressed sensing. IEEE Trans. Inf. Theory 52, 1289–1306 (2006)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  3. Wu, J., Liu, F., Jiao, L.C., Wang, X.: Multivariate compressive sensing for image reconstruction in the wavelet domain: using scale mixture models. IEEE Trans. Image Process. 20, 3483–3494 (2011)

    Article  MathSciNet  Google Scholar 

  4. Tan, J., Ma, Y., Baron, D.: Compressive imaging via approximate message passing with image denoising. IEEE Trans. Sig. Process. 63, 2085–2092 (2015)

    Article  MathSciNet  Google Scholar 

  5. Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. In: Eleventh International Conference of the Center for Nonlinear Studies on Experimental Mathematics: Computational Issues in Nonlinear Science: Computational Issues in Nonlinear Science, pp. 259–268. Elsevier, Amsterdam (1992)

    Google Scholar 

  6. Huang, J., Zhang, S., Metaxas, D.: Efficient MR image reconstruction for compressed MR imaging. Med. Image Anal. 15, 670–679 (2011)

    Article  Google Scholar 

  7. Xia, Z., Lv, R., Zhu, Y., Ji, P., Sun, H., Shi, Y.: Fingerprint liveness detection using gradient-based texture features. Sig. Image Video Process. 11, 381–388 (2017)

    Article  Google Scholar 

  8. Chen, C., Junzhou, H.: Exploiting the wavelet structure in compressed sensing MRI. Magn. Reson. Imaging 32, 1377–1389 (2014)

    Article  Google Scholar 

  9. Wang, M., Wu, X., Jing, W., He, X.: Reconstruction algorithm using exact tree projection for tree-structured compressive sensing. IET Sig. Process. 10, 566–573 (2016)

    Article  Google Scholar 

  10. Som, S., Schniter, P.: Compressive imaging using approximate message passing and a Markov-Tree prior. IEEE Trans. Sig. Process. 60, 3439–3448 (2012)

    Article  MathSciNet  Google Scholar 

  11. Zhang, X., Bai, T., Meng, H., Chen, J.: Compressive sensing-based ISAR imaging via the combination of the sparsity and nonlocal total variation. IEEE Geosci. Remote Sens. Lett. 11, 990–994 (2014)

    Article  Google Scholar 

  12. Dong, W., Shi, G., Wu, X., Zhang, J.: A learning-based method for compressive image recovery. J. Vis. Commun. Image Represent. 24, 1055–1063 (2013)

    Article  Google Scholar 

  13. Dong, W., Shi, G., Li, X., Ma, Y., Huang, F.: Compressive sensing via nonlocal low-rank regularization. IEEE Trans. Image Process. 23, 3618–3632 (2014)

    Article  MathSciNet  Google Scholar 

  14. Metzler, C.A., Maleki, A., Baraniuk, R.G.: From denoising to compressed sensing. IEEE Trans. Inf. Theory 62, 5117–5144 (2016)

    Article  MATH  MathSciNet  Google Scholar 

  15. Metzler, C.A., Maleki, A., Baraniuk, R.G.: BM3D-AMP: a new image recovery algorithm based on BM3D denoising. In: IEEE International Conference on Image Processing (ICIP), pp. 3116–3120. IEEE Press, New York (2015)

    Google Scholar 

  16. Zhang, J., Zhao, D., Zhao, C., Xiong, R., Ma, S., Gao, W.: Image compressive sensing recovery via collaborative sparsity. IEEE J. Emerg. Sel. Top. Circuits Syst. 2, 380–391 (2012)

    Article  Google Scholar 

  17. Zhou, Z., Wang, Y., Wu, Q., Yang, C., Sun, X.: Effective and efficient global context verification for image copy detection. IEEE Trans. Inf. Forensics Secur. 12, 48–63 (2017)

    Article  Google Scholar 

  18. Metzler, C.A., Maleki, A., Baraniuk, R.G.: From denoising to compressed sensing. IEEE Trans. Inf. Theory 62, 5117–5144 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  19. Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.: Image denoising by sparse 3D transform-domain collaborative filtering. IEEE Trans. Image Process. 16, 2080–2095 (2007)

    Article  MathSciNet  Google Scholar 

  20. Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2, 183–202 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  21. Hosseini, M.S., Plataniotis, K.N.: High-accuracy total variation with application to compressed video sensing. IEEE Trans. Image Process. 23, 3869–3884 (2014)

    Article  MathSciNet  Google Scholar 

  22. Ling, Q., Shi, W., Wu, G., Ribeiro, A.: DLM: decentralized linearized alternating direction method of multipliers. IEEE Trans. Sig. Process. 63, 4051–4064 (2015)

    Article  MathSciNet  Google Scholar 

  23. Yin, W., Osher, S., Goldfarb, D., Darbon, J.: Bregman iterative algorithms for L1-minimization with applications to compressed sensing. SIAM J. Imaging Sci. 1, 143–168 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  24. Qiao, T., Li, W., Wu, B.: A new algorithm based on linearized Bregman Iteration with generalized inverse for compressed sensing. Circ. Syst. Sig. Process. 33, 1527–1539 (2014)

    Article  MathSciNet  Google Scholar 

  25. Daubechies, I., Defriese, M., DeMol, C.: An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun. Pure Appl. Math. 57, 1413–1457 (2004)

    Article  MathSciNet  Google Scholar 

  26. Afonso, M., Bioucas-Dias, J., Figueiredo, M.: Fast image recovery using variable splitting and constrained optimization. IEEE Trans. Image Process. 19, 2345–2356 (2010)

    Article  MATH  MathSciNet  Google Scholar 

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Acknowledgments

This work is partially supported by the National Natural Science Foundation of China (No. 61302120), the Science and Technology Planning Project of Guangdong Province (No. 2017A020214011), the Fundamental Research Funds for the Central Universities (No. 2017MS039), the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20130172120045), and the supports of the Priority Academic Program Development of Jiangsu Higher Education Institutions, Jiangsu Collaborative Innovation Center on Atmospheric Environment and Equipment Technology (No. KJR16237). The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.

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Authors and Affiliations

  1. School of Electronic and Information Engineering, South China University of Technology, Guangzhou, 510641, China

    Lingjun Liu, Weiyu Yu & Cui Yang

  2. School of Electronic and Information Engineering, Nanjing University of Information Science & Technology, Ningliu Road, Nanjing, 210044, China

    Lingjun Liu & Weiyu Yu

Authors
  1. Lingjun Liu
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  2. Weiyu Yu
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  3. Cui Yang
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Corresponding author

Correspondence to Weiyu Yu .

Editor information

Editors and Affiliations

  1. Nanjing University of Information Science and Technology, Nanjing, China

    Xingming Sun

  2. National Dong Hwa University, Shoufeng, Taiwan

    Han-Chieh Chao

  3. China Information Technology Security Evaluation Center, Nanjing, China

    Xingang You

  4. Department of Computer Science, Purdue University, West Lafayette, Indiana, USA

    Elisa Bertino

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Liu, L., Yu, W., Yang, C. (2017). Adaptive Hybrid Wavelet Regularization Method for Compressive Imaging. In: Sun, X., Chao, HC., You, X., Bertino, E. (eds) Cloud Computing and Security. ICCCS 2017. Lecture Notes in Computer Science(), vol 10603. Springer, Cham. https://doi.org/10.1007/978-3-319-68542-7_39

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  • DOI: https://doi.org/10.1007/978-3-319-68542-7_39

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-68541-0

  • Online ISBN: 978-3-319-68542-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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