Skip to main content
SpringerLink
Log in

Image encryption using sparse coding and compressive sensing

  • Published:
Multidimensional Systems and Signal Processing Aims and scope Submit manuscript

Abstract

An encryption algorithm based on sparse coding and compressive sensing is proposed. Sparse coding is used to find the sparse representation of images as a linear combination of atoms from an overcomplete learned dictionary. The overcomplete dictionary is learned using K-SVD, utilizing non-overlapping patches obtained from a set of images. Compressed sensing is used to sample data at a rate below the Nyquist rate. A Gaussian measurement matrix compressively samples the plain image. As these measurements are linear, chaos based permutation and substitution operations are performed to obtain the cipher image. Bit-level scrambling and block substitution is done to confuse and diffuse the measurements. Simulation results verify the performance of the proposed technique against various statistical attacks.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Notes

  1. http://decsai.ugr.es/cvg/CG/base.htm.

  2. http://www.cs.technion.ac.il/~ronrubin/software.html.

References

  • Aharon, M., Elad, M., & Bruckstein, A. (2006). K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation. IEEE Transactions on Signal Processing, 54(11), 4311–4322.

    Article  MATH  Google Scholar 

  • Ashwini, K., & Amutha, R. (2018). Compressive sensing based simultaneous fusion and compression of multi-focus images using learned dictionary. Multimedia Tools and Applications, 77(19), 25889–25904.

    Article  Google Scholar 

  • Baraniuk, R. (2007). Compressive sensing [Lecture Notes]. IEEE Signal Processing Magazine, 24, 118–121.

    Article  Google Scholar 

  • Cambareri, V., Mangia, M., Pareschi, F., Rovatti, R., & Setti, G. (2015). On known-plaintext attacks to a compressed sensing-based encryption: A quantitative analysis. IEEE Transactions on Information Forensics and Security, 10(10), 2182–2195.

    Article  MATH  Google Scholar 

  • Candes, E., & Wakin, M. (2008). An introduction to compressive sampling. IEEE Signal Processing Magazine, 25(2), 21–30.

    Article  Google Scholar 

  • Candes, E. J. (2008). The restricted isometry property and its implications for compressed sensing. Comptes Rendus Mathematique, 346(9–10), 589–592.

    Article  MathSciNet  MATH  Google Scholar 

  • Chen, T., Zhang, M., Wu, J., Yuen, C., & Tong, Y. (2016). Image encryption and compression based on kronecker compressed sensing and elementary cellular automata scrambling. Optics & Laser Technology, 84, 118–133.

    Article  Google Scholar 

  • Donoho, D. L. (2006). Compressed sensing. IEEE Transactions on Information Theory, 52(4), 1289–1306.

    Article  MathSciNet  MATH  Google Scholar 

  • Engan, K., Skretting, K., & Husøy, J. H. (2007). Family of iterative LS-based dictionary learning algorithms, ILS-DLA, for sparse signal representation. Digital Signal Processing, 17(1), 32–49.

    Article  Google Scholar 

  • Hanis, S., & Amutha, R. (2019). A fast double-keyed authenticated image encryption scheme using an improved chaotic map and a butterfly-like structure. Nonlinear Dynamics, 95(1), 421–432.

    Article  Google Scholar 

  • Hu, G., Xiao, D., Wang, Y., & Xiang, T. (2017). An image coding scheme using parallel compressive sensing for simultaneous compression-encryption applications. Journal of Visual Communication and Image Representation, 44, 116–127.

    Article  Google Scholar 

  • Huang, R., Rhee, K. H., & Uchida, S. (2014). A parallel image encryption method based on compressive sensing. Multimedia Tools and Applications, 72(1), 71–93.

    Article  Google Scholar 

  • Huang, R., & Sakurai, K. (2011). A robust and compression-combined digital image encryption method based on compressive sensing. In Proceedings: 7th International Conference on Intelligent Information Hiding and Multimedia Signal Processing, IIHMSP 2011, pp. 105–108.

  • Huang, W., & Jing, Z. (2007). Evaluation of focus measures in multi-focus image fusion. Pattern Recognition Letters, 28(4), 493–500.

    Article  Google Scholar 

  • Olshausen, B. A., & Field, D. J. (1997). Sparse coding with an overcomplete basis set: A strategy employed by V1? Vision Research, 37(23), 3311–3325.

    Article  Google Scholar 

  • Orsdemir, A., Altun, H. O., Sharma, G., & Bocko, M. F. (2008). On the security and robustness of encryption via compressed sensing. In Proceedings: IEEE Military Communications Conference MILCOM.

  • Ponuma, R., & Amutha, R. (2018). Compressive sensing and chaos-based image compression encryption. In Advances in Soft Computing and Machine Learning in Image Processing, pp. 373–392. Springer.

  • Ponuma, R., & Amutha, R. (2018b). Compressive sensing based image compression-encryption using novel 1d-chaotic map. Multimedia Tools and Applications, 77(15), 19209–19234.

    Article  Google Scholar 

  • Ponuma, R., & Amutha, R. (2018). Encryption of image data using compressive sensing and chaotic system. Multimedia Tools and Applications. https://doi.org/10.1007/s11042-018-6745-3.

  • Skretting, K., & Engan, K. (2010). Recursive least squares dictionary learning algorithm. IEEE Transactions on Signal Processing, 58(4), 2121–2130.

    Article  MathSciNet  MATH  Google Scholar 

  • Tropp, J. A., & Gilbert, A. C. (2007). Signal recovery from random measurements via orthogonal Matching Pursuit - Semantic Scholar. IEEE Transactions on Information Theory, 53(12), 4655–4666.

    Article  MathSciNet  MATH  Google Scholar 

  • Xu, L., Li, Z., Li, J., & Hua, W. (2016). A novel bit-level image encryption algorithm based on chaotic maps. Optics and Lasers in Engineering, 78, 17–25.

    Article  Google Scholar 

  • Zahmoul, R., Ejbali, R., & Zaied, M. (2017). Image encryption based on new Beta chaotic maps. Optics and Lasers in Engineering, 96, 39–49.

    Article  Google Scholar 

  • Zhang, Y., Zhou, J., Chen, F., Zhang, L. Y., Wong, K.-W., He, X., et al. (2016). Embedding cryptographic features in compressive sensing. Neurocomputing, 205, 472–480.

    Article  Google Scholar 

  • Zhou, N., Pan, S., Cheng, S., & Zhou, Z. (2016). Image compression-encryption scheme based on hyper-chaotic system and 2D compressive sensing. Optics & Laser Technology, 82, 121–133.

    Article  Google Scholar 

  • Zhou, N., Zhang, A., Wu, J., Pei, D., & Yang, Y. (2014a). Novel hybrid image compression-encryption algorithm based on compressive sensing. Optik, 125(18), 5075–5080.

    Article  Google Scholar 

  • Zhou, N., Zhang, A., Zheng, F., & Gong, L. (2014b). Novel image compression-encryption hybrid algorithm based on key-controlled measurement matrix in compressive sensing. Optics & Laser Technology, 62, 152–160.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of ECE, Sri Sivasubramaniya Nadar College of Engineering, Chennai, India

    R. Ponuma & R. Amutha

Authors
  1. R. Ponuma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Amutha
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. Ponuma.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ponuma, R., Amutha, R. Image encryption using sparse coding and compressive sensing. Multidim Syst Sign Process 30, 1895–1909 (2019). https://doi.org/10.1007/s11045-019-00634-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11045-019-00634-x

Keywords

Search

Navigation