Comparison between Fourier and Wavelets Transforms in Biospeckle Signals


The dynamic speckle is a non-destructive optical technique that has been used as a tool for the characterization of the biological activity and several studies are conducted to obtain for more information about the correspondence of the observed phenomena and their expressions in the interference images. Analysis in the frequency domain has been considered as powerful alternative, and although there are works using Fourier transform in the frequency analysis of the biospeckle signals, the majority presents the wavelet transform as tool for spectral analysis. In turn, there are still doubts if the Fourier transform is not enough for the analysis of the biospeckle, which would enable the reduction of processing time since an operation is computationally simpler. In this context, the present study aims to compare the constituents’ parts of the speckle signal according to Fourier and wavelet transforms for numerical analysis. The comparative analysis based on the absolute values of the differences technique (AVD) was carried out for performance evaluation of the Fourier and wavelet transforms, in which the speckle signals were decomposed spectrally and subsequently reconstructed with the elimination of specific frequency bands. Results showed that the wavelet transform allowed more information about signals constituents of the dynamic speckle, emphasizing its use instead of the Fourier transform, which in turn was restricted the situations in which the only interest is to know the spectral content of the data.

Share and Cite:

K. Ribeiro, R. Júnior, T. Sáfadi and G. Horgan, "Comparison between Fourier and Wavelets Transforms in Biospeckle Signals," Applied Mathematics, Vol. 4 No. 11C, 2013, pp. 11-22. doi: 10.4236/am.2013.411A3003.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Y. Zhao, J. Wang, X. Wu, F. W. Williams and R. J. Schmidt, “Point-Wise and Whole-Field Laser Speckle Intensity Fluctuation Measurements Applied to Botanical Specimens,” Optics and Lasers in Engineering, Vol. 28, No. 6, 1997, pp. 443-456.
[2] H. J. Rabal and R. A. Braga, “Dynamic Laser Speckle and Applications,” CRC Press, New York, 2008.
[3] A. P. Rathnayake, H. Kadono, S. Toyooka and M. Miwa, “A Novel Optical Interference Technique to Measure Minute Root Elongations of Japanese Red Pine (Pinusdensiflora Seibold & Zucc.) Seedlings Infected with Ectomycorrhizal Fungi,” Environmental and Experimental Botany, Vol. 64, No. 3, 2008, pp. 314-321.
[4] R. A. Braga, L. Dupuy, M. Pasqual and R. R. Cardoso, “Live Biospeckle Laser Imaging of Root Tissue,” European Biophysics, Vol. 38, No. 5, 2009, pp. 679-686.
[5] R. R. Cardoso, A. G. Costa, C. M. B. Nobre and R. A. Braga, “Frequency Signature of Water Activity by Biospeckle Laser,” Optics Communications, Vol. 284, No. 8, 2011, pp. 2131-2136.
[6] A. Zdunek and W. B. Herppich, “Relation of Biospeckle Activity with Chlorophyll Content in Apples,” Postharvest Biology Technology, Vol. 64, No. 1, 2012, pp. 58-63.
[7] I. Passoni, A. Dai Pra, H. J. Rabal, M. Trivi and R. Arizaga, “Dynamic Speckle Processing Using Wavelets Based Entropy,” Optics Communications, Vol. 246, No. 1-3, 2005, pp. 219-228.
[8] R. M. Costa, T. Sáfadi, G. F. Rabelo and R. A. Braga, “Técnicas Estatísticas Aplicadas em Imagens do Speckle Dinamico,” Revista Brasileira de Biometria, Vol. 28, No. 2, 2010, pp. 27-39.
[9] G. F. Rabelo, A. M. Enes, R. A. Braga and I. M. Dal Fabbro, “Frequency Response of Biospeckle Laser Images of Bean Seeds Contaminated by Fungi,” Biosystems Engineering, Vol. 110, No. 3, 2011, pp. 297-301.
[10] G. H. Sendra, R. Arizaga, H. Rabal and M. Trivi, “Decomposition of Biospeckle Images in Temporary Spectral Bands,” Optics Letters, Vol. 30, No. 13, 2005, pp. 1641-1643.
[11] M. D. Z. Ansari and A. K. Nirala, “Assessment of the BioActivity Using the Methods of Inertia Moment and Absolute Value of the Differences,” Optiks—International Journal for Light and Electron Optics, Vol. 124, No. 15, 2013, pp. 2180-2186.
[12] G. Oulamara, J. Tribillon and J. Duvernoy, “Biological Activity Measurements on Botanical Specimen Surfaces Using a Temporal Decorrelation Effect of Laser Speckle,” Journal of Moderns Optics, Vol. 36, No. 2, 1989, pp. 136-179.
[13] R. Arizaga, M. Trivi and H. Rabal, “Speckle Time Evolution Characterization by the Co-Occurrence Matrix Analysis,” Optics and Laser Technology, Vol. 31, No. 2, 1999, pp. 163-169.
[14] R. A. Braga, I. M. Dal Fabbro, F. M. Borém, G. F. Rabelo, R. Arizaga, H. Rabal and M. Trivi, “Assessment of Seed Viability by Laser Speckle Techniques,” Biosystems Engineering, Vol. 86, No. 3, 2003, pp. 287-294.
[15] R. A. Braga, C. M. B. Nobre, A. G. Costa, T. Sáfadi and F. M. Costa, “Evaluation of Activity through Dynamic Laser Speckle Using the Absolute Value of the Differences,” Optics Communications, Vol. 284, No. 2, 2011, pp. 646-650.
[16] P. A. Morettin, “Ondas e Ondeletas,” EDUSP, Sao Paulo, 1999.
[17] M. Sifuzzaman, M. R. Islam and M. Z. Ali, “Application of Wavelet Transform and Its Advantages Compared to Fourier Transform,” Journal of Physical Sciences, Vol. 13, No. 1, 2009, pp. 121-134.
[18] A. Graps, “An Introduction to Wavelets,” Computation Science and Engineering, IEEE, Vol. 2, No. 2, 1995, pp. 50-61.
[19] C. Torrence and G. P. Compo, “A Practical Guide to Wavelet Analysis,” Bulletin of the American Meteorological Society, Vol. 79, No. 1, 1998, pp. 61-78.<0061:APGTWA>2.0.CO;2
[20] H. R. Karimi, W. Pawlus and K. G. Robbersmyr, “Signal Reconstruction, Modeling and Simulation of a Vehicle Full-Scale Crash Test Based Morlet Wavelets,” Neurocomputing, Vol. 93, No. 15, 2012, pp. 88-99.
[21] M. Farge, “Wavelet Transforms and Their Applications to Turbulence,” Annual Review of Fluid Mechanics, Vol. 24, No. 1, 1992, pp. 395-457.
[22] C. E. Shannon, “Communication in the Presence of Noise,” Proceedings of the IRE, Vol. 37, No. 1, 1949, pp. 10-21.
[23] M. M. Silva, J. R. A. Nozela, M. J. Chaves, R. A. Braga and H. Rabal, “Optical Mouse Acting as Biospeckle Sensor,” Optics Communications, Vol. 284, No. 7, 2011, pp. 1798-1802.
[24] L. Polansky, G. Wittemyer, P. C. Cross, C. J. Tambling and W. M. Getz, “From Moonlight to Movement and Synchronized Randomness: Fourier and Wavelet Analyses of Animal Location Time Series Data,” Ecology, Vol. 91, No. 5, 2010, pp. 1506-1518.
[25] H. Sendra, S. Murialdo and L. Passoni, “Dynamic Laser Speckle to Detect Motile Bacterial Response of Pseudomonas Aeruginosa,” Journal of Physics: Conference Series, Vol. 90, No. 1, 2007, pp. 1-6.

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.