Skip to main content
Log in

Multifocus and multispectral image fusion based on pixel significance using discrete cosine harmonic wavelet transform

  • Original Paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript


The energy compaction and multiresolution properties of wavelets have made the image fusion successful in combining important features such as edges and textures from source images without introducing any artifacts for context enhancement and situational awareness. The wavelet transform is visualized as a convolution of wavelet filter coefficients with the image under consideration and is computationally intensive. The advent of lifting-based wavelets has reduced the computations but at the cost of visual quality and performance of the fused image. To retain the visual quality and performance of the fused image with reduced computations, a discrete cosine harmonic wavelet (DCHWT)-based image fusion is proposed. The performance of DCHWT is compared with both convolution and lifting-based image fusion approaches. It is found that the performance of DCHWT is similar to convolution-based wavelets and superior/similar to lifting-based wavelets. Also, the computational complexity (in terms of additions and multiplications) of the proposed method scores over convolution-based wavelets and is competitive to lifting-based wavelets.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others





Discrete wavelet transform


Wavelet transform


Multiresolution discrete cosine transform


Harmonic wavelet transform


Fourier transform


Fast Fourier transform


Discrete Fourier transform


Harmonic wavelet coefficient


Discrete cosine transform


Inverse DCT


Discrete cosine transform harmonic wavelet transform


Discrete cosine harmonic wavelet transform


Discrete cosine harmonic wavelet coefficients


  1. Blum R., Liu Z.: Multi-sensor Image Fusion and Its Applications. CRC Press, London (2005)

    Google Scholar 

  2. Shah, P., Merchant, S.N., Desai, U.B.: Multifocus and multispectral image fusion based on pixel significance using multiresolution decomposition. J. SIViP (2011). doi: 10.1007/s11760-011-0219-7

  3. Shah P., Merchant S.N., Desai U.B.: Fusion of surveillance images in infrared and visible band using curvelet, wavelet and wavelet packet transform. Int. J. Wavelets. Multiresolution Inform. Process. 8(2), 271–292 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Qu G., Zhang D., Yan P.: Medical image fusion by wavelet transform modulus maxima. Opt. Express 9(4), 184–190 (2001)

    Article  Google Scholar 

  5. Licai, M.Y., Xin, L., Yucui, Y.: Medical image fusion based on wavelet packet transform and self-adaptive operator. In: Proceedings of International Conference on Bioinformatics and Biomedical Engineering (ICBBE), pp. 2647–2650 May (2008)

  6. Petrovic, V.: Multisensor Pixel-Level Image Fusion PhD Thesis. Department of Imaging Science and Biomedical Engineering Manchester School of Engineering, United Kingdom (2001)

  7. Hamza A.B., He Y., Krim H., Willsky A.: A multiscale approach to pixel-level image fusion. Integr. Comput. Aided Eng. 12(2), 135–146 (2005)

    Google Scholar 

  8. Li H., Manjunath B.S., Mitra S.K.: Multisensor image fusion using the wavelet transform graph. Models Image Process. 57(3), 235–245 (1995)

    Article  Google Scholar 

  9. Sasikala M., Kumaravel M.: A comparative analysis of feature-based image fusion method. Inf. Tech. J. 6(8), 1224–1230 (2007)

    Article  Google Scholar 

  10. Tao Q., Veldhuis R.: Threshold-optimized decision-level fusion and its application to biometrics. Pattern Recogn. 42, 823–836 (2009)

    Article  Google Scholar 

  11. Carper J.W., Lilles T.M., Kiefer R.W.: The use of intensity-hue saturation transformations for merging SPOT panchromatic and multi-spectra image data. Photogr. Eng. Remote Sens. 56, 459–467 (1990)

    Google Scholar 

  12. Toet A.: Hierarchical image fusion. Mach. Vis. Appl. 3(1), 1–11 (1990)

    Article  Google Scholar 

  13. Haeberli, P.: A Multi-focus Method for Controlling Depth of Field. Grafic Obscura (1994)

  14. Daubechies, I.: Ten Lectures on Wavelets. CBMS-NSF Regional Conference on Series in Applied Mathematics, 61, 2nd edn. SIAM, Philadelphia (1992)

  15. Zhi-guo, J., Dong-bing, H., Jin, C., Xiao-kuan, Z.: A Wavelet based Algorithm for Multi-focus Micro-image Fusion. In: Proceedings of International Conference on Image and Graphics (ICIG), pp. 176–179, Dec (2004)

  16. Ranjith T., Ramesh C.: A lifting wavelet transform based algorithm for multi-sensor image fusion. CRL Tech. J. 3(3), 19–22 (2001)

    Google Scholar 

  17. Hill, P., Canagaraj, N., Bull, D.: Image Fusion using Complex Wavelets. In: Proc. of British Machine Vision Conference (BMVC), pp. 487–496, Sep (2002)

  18. Du Y., Vachon P.W., Vander Sanden J.J.: Satellite image fusion with multi-scale wavelet analysis for marine applications. Can. J. Remote Sens. 29(1), 14–23 (2003)

    Article  Google Scholar 

  19. Wang Z., Ziou D., Armenakis C., Li D., Li Q.: A comparative analysis of image fusion methods. In: IEEE Trans. Geosci. Remote Sens. 43(6), 1392–1402 (2005)

    Google Scholar 

  20. Zheng S., Shi W.-Z., Liu J., Zhu G.-X., Tian J.-W.: Multisource image fusion method using support value transform. In: IEEE Trans. Image Process. 16(7), 1831–1839 (2007)

    Article  MathSciNet  Google Scholar 

  21. Li S., Kwok J.T., Wang Y.: Multifocus image fusion using artificial neural networks. Pattern Recogn. Lett. 23, 985–997 (2002)

    Article  MATH  Google Scholar 

  22. Hao Y., Sun Z., Tan T.: Comparative studies on multispectral palm image fusion for biometrics. ACCV, Part II, LNCS 4844, 12–21 (2007)

    Google Scholar 

  23. Arivazhagan S., Ganesan L., Subash Kumar T.G.: A modified statistical approach for image fusion using wavelet transform. J. SIViP 3(2), 137–144 (2009)

    Article  Google Scholar 

  24. Shah, P., Srikanth, T.V., Merchant, S.N., Desai, U.B.: A novel multifocus image fusion scheme based on pixel significance using wavelet transform. In: Proceedings of Image, Video, and Multidimensional Signal Process (IVMSP), pp. 54–59, Aug (2011)

  25. Rahman S.M.M., Ahmad M.O., Swamy M.N.S.: Contrast-based fusion of noisy images using discrete wavelet transform. IET Image Process. 4(5), 374–384 (2010). doi:10.1049/iet-ipr.2009.0163

    Article  MathSciNet  Google Scholar 

  26. Naidu V.P.S.: Discrete cosine transform-based image fusion. Def. Sci. J. 60(1), 48–54 (2010)

    Google Scholar 

  27. Newland D.E.: Harmonic wavelet analysis. Proc. R. Soc. Lond. A: Math. Phys. Eng. Sci. 443(1917), 203–225 (1993)

    Article  MATH  Google Scholar 

  28. Newland, D.E.: Time-frequency and time-scale signal analysis by harmonic Wavelets. In: Proceedings of European Conference on Signal Analysis and Prediction, pp. 53–59, Prague, Jun (1997)

  29. Newland D.E.: Random Vibrations, Spectral and Wavelets Analysis. 3rd edn. Longman, Singapore (1993)

    Google Scholar 

  30. Narasimhan, S.V., Harish, M.: Spectral estimation based on subband decomposition by harmonic wavelet transform and modified group delay. In: Proceedings of International Conference on Signal Processing and Communications (SPCOM), pp. 349–353, Bangalore, Dec (2004)

  31. Tezcan J.: Evolutionary power spectrum estimation using harmonic wavelets. J. Seism. Des. Anal. Struct. Chap. 6, 37–41 (1999)

    Google Scholar 

  32. Gurlzow T., Ludwig T., Heute U.: Spectral-subtraction speech enhancement in multirate systems with and without non-uniform and adaptive bandwidths. Signal Process. 83(8), 1613–1631 (2003)

    Article  Google Scholar 

  33. Shreyamsha Kumar, B.K., Prabhakar, B., Suryanarayana, K., Thilagavathi, V.: Harmonic wavelet based ISAR imaging for target identification. In: Proceedings of International Radar Symposium India (IRSI), pp. 343–348, Bangalore, Dec (2005)

  34. Shreyamsha Kumar B.K., Prabhakar B., Suryanarayana K., Thilagavathi V., Rajagopal R.: Target identification using harmonic wavelet based ISAR imaging. J. Appl. Signal Process. 2006, 1–13 (2006)

    Google Scholar 

  35. Cattani C.: Harmonic wavelets towards the solution of nonlinear PDE. Comput. Math. Appl. 50(8), 1191–1210 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  36. Shreyamsha Kumar, B.K.: Group Delay Functions for Time Frequency Representation and Spectral Estimation, M.Tech Thesis, Department of Electronics & Communication Engineering, National Institute of Technology Karnataka, Surathkal (2004)

  37. Narasimhan, S.V., Shreyamsha Kumar, B.K.: Harmonic wavelet transform signal decomposition and modified group delay for improved Wigner–Ville distribution. In: Proceedings of International Conference on Signal Processing and Communications (SPCOM), pp. 354–358, Bangalore, Dec (2004)

  38. Narasimhan, S.V., Harish, M.: Discrete cosine harmonic wavelet transform and its application to subband spectral estimation using modified group delay. In: Pai, B.R. Dr. (eds.) Proceedings of Conference in Honor of Dr. B. R. Pai. National Aerospace Laboratories, Bangalore (2004)

  39. Narasimhan S.V., Harish M., Haripriya A.R., Basumallick N.: Discrete cosine harmonic wavelet transform and its application to signal compression and subband spectral estimation using modified group delay. J. SIViP 3(1), 85–99 (2009). doi:10.1007/s11760-008-0062-7

    Article  MATH  Google Scholar 

  40. Shreyamsha Kumar B.K.: Image Denoising using Discrete Cosine Harmonic Wavelets. Technical Report, Sensor Signal Process. Group, Central Research Laboratory, Bangalore, Jul (2010)

  41. Shivamurti, M., Narasimhan, S.V.: Analytic discrete cosine harmonic wavelet transform (ADCHWT) and its application to signal/image denoising. In: Proceedings of International Conference on Signal Processing and Communications (SPCOM), pp. 1–5, Bangalore, Jul (2010)

  42. Narasimhan, S.V., Veena, S.: A new delayless subband adaptive filter based on discrete cosine harmonic wavelet transform (CHWT). In: Proceedings of International Conference on Signal Processing and Communications (SPCOM), pp. 1–5, Bangalore, Jul (2010)

  43. Narasimhan S.V., Haripriya A.R., Shreyamsha Kumar B.K.: Improved Wigner–Ville distribution performance based on DCT/DFT harmonic wavelet transform and modified magnitude group delay. Signal Process. 88(1), 1–18 (2008)

    Article  MATH  Google Scholar 

  44. Raghuveer M.R., Bopardikar A.S.: Wavelet Transforms Introduction to Theory and Applications. Pearson Education Pte. Ltd., Delhi (2004)

    Google Scholar 

  45. Samar, V.J., Begleiter, H., Chapa, J.O., Raghuveer, M.R., Orlando, M., Chorlian, D.: Matched meyer neural wavelets for clinical and experimental analysis of auditory and visual evoked potentials. In: Proceedings of European Signal Processing Conference (EUSIPCO), pp. 387–390, Sep (1996)

  46. Cattani C.: Shannon wavelets theory. J. Math. Probl. Eng. 2009, 1–24 (2009). doi:10.1155/2008/164808

    Google Scholar 

  47. Cattani C.: Harmonic wavelet solutions of the Schrodinger equation. Int. J. Fluid Mech. Res. 30(5), 1–10 (2003)

    Article  MathSciNet  Google Scholar 

  48. Cattani C., Kudreyko A.: On the discrete harmonic wavelet transform. J. Math. Probl. Eng. 2008, 1–7 (2008). doi:10.1155/2008/687318

    MathSciNet  Google Scholar 

  49. Narasimhan S.V., Veena S.: Signal Processing: Principles and Implementation, Revised Edition. Narosa Publishing House Pvt. Ltd, India (2008)

    Google Scholar 

  50. Britanak V., Yip P.C., Rao K.R.: Discrete Cosine and Sine Transforms. 1st edn. Academic Press, Great Britain (2007)

    Google Scholar 

  51. Petrovic, V., Xydeas, C.: Objective image fusion performance characterization. In: Proceedings of International Conference on Computer Vision (ICCV), vol. 2, pp. 1866–1871, Oct (2005)

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to B. K. Shreyamsha Kumar.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shreyamsha Kumar, B.K. Multifocus and multispectral image fusion based on pixel significance using discrete cosine harmonic wavelet transform. SIViP 7, 1125–1143 (2013).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: