Technical Information

  • Rohit Thanki
  • Surekha Borra
Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)


This chapter presents various image transforms which are used in the present research work. This chapter also describes different encryption methods such as compressive sensing (CS)-based encryption and Arnold scrambling. Finally, some noise sequences used in the presented technique are described.


Redundant Discrete Wavelet Transform (RDWT) Fast Discrete Curvelet Transform (FDCuT) Finite Ridgelet Transform (FRT) Non-subsampled Contourlet Transform (NSCT) Encryption 


  1. 1.
    Jain A (1999) Fundamentals of digital image processing. Prentice Hall Inc, Upper Saddle River, NJzbMATHGoogle Scholar
  2. 2.
    Yan J (2009) Wavelet matrix. Department of Electrical and Computer Engineering, University of Victoria, Victoria, BCGoogle Scholar
  3. 3.
    Vidakovic B (1999) Statistical modelling by wavelets. Wiley, New York, pp 115–116CrossRefGoogle Scholar
  4. 4.
    Hiena T, Nakaoa Z, Chen Y (2006) Robust multi-logo watermarking by RDWT and ICA. Signal Process 86:2981–2993CrossRefGoogle Scholar
  5. 5.
    Lagzian S, Soryani M, Fathy M (2011) A new robust watermarking scheme based on RDWT – SVD. Int J Intell Inf Process 2(1):22–29Google Scholar
  6. 6.
    Candes E, Demanet L, Donoho D, Ying L (2006) Fast discrete curvelet transforms. SIAM Mult Model Sim 5(3):861–889MathSciNetCrossRefGoogle Scholar
  7. 7.
    Candes E, Donoho DL (2004) New tight frames of curvelets and optimal representations of objects with piecewise-C2 singularities. Commun Pure Appl Math 57:219–266CrossRefGoogle Scholar
  8. 8.
    Donoho D (2001) Ridge functions and orthonormal ridgelets. J Approx Theory 111(2):143–179MathSciNetCrossRefGoogle Scholar
  9. 9.
    Do M, Vetterli M (2000) Orthonormal finite ridgelet transform for image compression. In: Proceedings of the international conference on image processing (ICIP ’00), pp 367–370Google Scholar
  10. 10.
    Candes E, Donoho D (2000) A surprisingly effective non-adaptive representation for objects with edges, curves and surfaces. Vanderbilt University Press, Nashville, TNGoogle Scholar
  11. 11.
    Candes E (1998) Ridgelets theory and application. Ph.D. Thesis, Department of Statistics, Stanford University, Stanford, CAGoogle Scholar
  12. 12.
    AlZubi S, Islam N, Abbod M (2011) Multiresolution analysis using wavelet, ridgelet, and curvelet transforms for medical image segmentation. Int J Biomed Imaging 2011:18CrossRefGoogle Scholar
  13. 13.
    Candes E, Donoho D (1999) Ridgelets: a key to higher dimensional intermittency? Phil Trans R Soc A 357(1760):2495–2509MathSciNetCrossRefGoogle Scholar
  14. 14.
    He J (2006) A characterization of inverse Radon transform on the Laguerre hypergroup. J Math Anal Appl 318(1):387–395MathSciNetCrossRefGoogle Scholar
  15. 15.
    Dettori L, Semler L (2007) A comparison of wavelet, ridgelet and curvelet-based texture classification algorithms in computed tomography. Comput Biol Med 37(4):486–498CrossRefGoogle Scholar
  16. 16.
    Do M, Vetterli M (2005) The contourlet transform: an efficient directional multiresolution image representation. IEEE Trans Image Process 14(12):2091–2106CrossRefGoogle Scholar
  17. 17.
    Da Cunha AL, Zhou J, Do MN (2006) The nonsubsampled contourlet transform: theory, design, and applications. IEEE Trans Image Process 15(10):3089–3101CrossRefGoogle Scholar
  18. 18.
    Arnold VI, Avez A (1968) Ergodic problems in classical mechanics. Benjamin, New YorkzbMATHGoogle Scholar
  19. 19.
    Donoho D (2006) Compressed sensing. IEEE Trans Inf Theory 52(4):1289–1306MathSciNetCrossRefGoogle Scholar
  20. 20.
    Candes E, Wakin M (2008) An introduction to compressive sampling. IEEE Signal Process Mag 25(2):21–30CrossRefGoogle Scholar
  21. 21.
    Rachlin Y, Baron D (2008) The secrecy of compressed sensing measurements. In: The 46th Annual Allerton conference on communication, control, and computing. IEEE, pp 813–817Google Scholar
  22. 22.
    Orsdemir A, Altun HO, Sharma G, Bocko MF (2008) On the security and robustness of encryption via compressed sensing. In: 2008 I.E. military communications conference. MILCOM 2008. IEEE, pp 1–7Google Scholar
  23. 23.
    Agrawal S, Vishwanath S (2011) Secrecy using compressive sensing. In: 2011 I.E. information theory workshop (ITW). IEEE, pp 563–567Google Scholar
  24. 24.
    Hossein SA, Tabatabaei AE, Zivic N (2012) Security analysis of the joint encryption and compressed sensing. In: 2012 20th telecommunications forum (TELFOR). IEEE, pp 799–802Google Scholar
  25. 25.
    Zhang Y, Zhang LY, Zhou J, Liu L, Chen F, He X (2016) A review of compressive sensing in information security field. IEEE Access 4:2507–2519CrossRefGoogle Scholar
  26. 26.
    Tropp JA, Gilbert AC (2007) Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans Inf Theory 53(12):4655–4666MathSciNetCrossRefGoogle Scholar
  27. 27.
    Borra S, Thanki R, Dey N, Borisagar K (2018) Secure transmission and integrity verification of color radiological images using fast discrete curvelet transform and compressive sensing. Smart Health.Google Scholar
  28. 28.
    Mancini C, Bruce R (2009) OP amps for everyone. Texas Instruments, pp 10–11Google Scholar

Copyright information

© The Author(s), under exclusive license to Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Rohit Thanki
    • 1
  • Surekha Borra
    • 2
  1. 1.C. U. Shah UniversityWadhwan CityIndia
  2. 2.Department of Electronics & Communication EngineeringK.S. Institute of TechnologyBengaluruIndia

Personalised recommendations