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A wavelet filter comparison on multiple datasets for signal compression and denoising

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Abstract

In this paper, we explicitly analyze the performance effects of several orthogonal and bi-orthogonal wavelet families. For each family, we explore the impact of the filter order (length) and the decomposition depth in the multiresolution representation. In particular, two contexts of use are examined: compression and denoising. In both cases, the experiments are carried out on a large dataset of different signal kinds, including various image sets and 1D signals (audio, electrocardiogram and seismic). Results for all the considered wavelets are shown on each dataset. Collectively, the study suggests that a meticulous choice of wavelet parameters significantly alters the performance of the above mentioned tasks. To the best of authors’ knowledge, this work represents the most complete analysis and comparison between wavelet filters. Therefore, it represents a valuable benchmark for future works.

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Notes

  1. For conciseness sake, the curves associated to the SD aerials and textures are not shown here. However, they can be reproduced from Gnutti (2019). We report that they are consistent with the ones provided in this paper.

  2. Again, refer to Gnutti (2019) for the HD high precision image set performance.

References

  • Daubechies, I. (1992). Ten Lectures on Wavelets. Philadelphia, PA, USA: Society for Industrial and Applied Mathematics.

    Book  MATH  Google Scholar 

  • Vetterli, M., & Kovačevic, J. (1995). Wavelets and Subband Coding. Upper Saddle River, NJ, USA: Prentice-Hall Inc.

    MATH  Google Scholar 

  • Mallat, S. (1999). A wavelet tour of signal processing. New York: Elsevier.

    MATH  Google Scholar 

  • Ohm, J. (1994). Three-dimensional subband coding with motion compensation. IEEE Transactions on Image Processing, 3(5), 559–571.

    Article  Google Scholar 

  • Lewis, A. S., & Knowles, G. (1992). Image compression using the 2-d wavelet transform. IEEE Transactions on Image Processing, 1(2), 244–250.

    Article  Google Scholar 

  • Antonini, M., Barlaud, M., Mathieu, P., & Daubechies, I. (1992). Image coding using wavelet transform. IEEE Transactions on Image Processing, 1(2), 205–220.

    Article  Google Scholar 

  • DeVore, R. A., Jawerth, B., & Lucier, B. J. (1992). Image compression through wavelet transform coding. IEEE Transactions on Information Theory, 38(2), 719–746.

    Article  MathSciNet  MATH  Google Scholar 

  • Usevitch, B. E. (2001). A tutorial on modern lossy wavelet image compression: Foundations of jpeg 2000. IEEE Signal Processing Magazine, 18(5), 22–35.

    Article  Google Scholar 

  • Shapiro, J. M. (1993). Embedded image coding using zerotrees of wavelet coefficients. IEEE Transactions on Signal Processing, 41(12), 3445–3462.

    Article  MATH  Google Scholar 

  • Said, A., Pearlman, W. A., et al. (1996). A new, fast, and efficient image codec based on set partitioning in hierarchical trees. IEEE Transactions on Circuits and Systems for Video Technology, 6(3), 243–250.

    Article  Google Scholar 

  • Lazzaroni, F., Leonardi, R., & Signoroni, A. (2003). High-performance embedded morphological wavelet coding. IEEE Signal Processing Letters, 10(10), 293–295.

    Article  Google Scholar 

  • Qureshi, M. A., & Deriche, M. (2016). A new wavelet based efficient image compression algorithm using compressive sensing. Multimedia Tools and Applications, 75(12), 6737–6754.

    Article  Google Scholar 

  • Deng, C., Lin, W., Lee, B., & Lau, C. T. (2012). Robust image coding based upon compressive sensing. IEEE Transactions on Multimedia, 14(2), 278–290.

    Article  Google Scholar 

  • Karami, A., Yazdi, M., & Mercier, G. (2012). Compression of hyperspectral images using discerete wavelet transform and tucker decomposition. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 5(2), 444–450.

    Article  Google Scholar 

  • Bruylants, T., Munteanu, A., & Schelkens, P. (2015). Wavelet based volumetric medical image compression. Signal Processing: Image Communication, 31, 112–133.

    Google Scholar 

  • Leonardi, R., & Signoroni, A. (2006). Cyclostationary error analysis and filter properties in a 3d wavelet coding framework. Signal Processing Image Communication, 21(8), 653–675.

    Article  Google Scholar 

  • Adami, N., Signoroni, A., & Leonardi, R. (2007). State-of-the-art and trends in scalable video compression with wavelet-based approaches. IEEE Transactions on Circuits and Systems for Video Technology, 17(9), 1238–1255.

    Article  Google Scholar 

  • Luisier, F., Vonesch, C., Blu, T., & Unser, M. (2010). Fast interscale wavelet denoising of poisson-corrupted images. Signal Processing, 90(2), 415–427.

    Article  MATH  Google Scholar 

  • Luisier, F., Blu, T., & Unser, M. (2011). Image denoising in mixed poisson-gaussian noise. IEEE Transactions on Image Processing, 20(3), 696–708.

    Article  MathSciNet  MATH  Google Scholar 

  • Parrilli, S., Poderico, M., Angelino, C. V., & Verdoliva, L. (2012). A nonlocal sar image denoising algorithm based on llmmse wavelet shrinkage. IEEE Transactions on Geoscience and Remote Sensing, 50(2), 606–616.

    Article  Google Scholar 

  • Lai, C., & Tsai, C. (2010). Digital image watermarking using discrete wavelet transform and singular value decomposition. IEEE Transactions on Instrumentation and Measurement, 59(11), 3060–3063.

    Article  Google Scholar 

  • Guerrini, F., Okuda, M., Adami, N., & Leonardi, R. (2011). High dynamic range image watermarking robust against tone-mapping operators. IEEE Transactions on Information Forensics and Security, 6(2), 283–295.

    Article  Google Scholar 

  • Demirel, H., & Anbarjafari, G. (2011). Image resolution enhancement by using discrete and stationary wavelet decomposition. IEEE Transactions on Image Processing, 20(5), 1458–1460.

    Article  MathSciNet  MATH  Google Scholar 

  • Demirel, H., & Anbarjafari, G. (2011). Discrete wavelet transform-based satellite image resolution enhancement. IEEE Transactions on Geoscience and Remote Sensing, 49(6), 1997–2004.

    Article  MATH  Google Scholar 

  • Singh, R., & Khare, A. (2014). Fusion of multimodal medical images using daubechies complex wavelet transform - A multiresolution approach. Information Fusion, 19, 49–60.

    Article  Google Scholar 

  • Yang, Y., Park, D. S., Huang, S., & Rao, N. (2010). Medical image fusion via an effective wavelet-based approach. EURASIP Journal of Advance Signal Process, 44(1–44), 13.

    Google Scholar 

  • Li, S., Yang, B., & Hu, J. (2011). Performance comparison of different multi-resolution transforms for image fusion. Information Fusion, 12(2), 74–84.

    Article  Google Scholar 

  • Bhat, V., Sengupta, I., & Das, A. (2010). An adaptive audio watermarking based on the singular value decomposition in the wavelet domain. Digital Signal Processing, 20(6), 1547–1558.

    Article  Google Scholar 

  • Kabir, M. A., & Shahnaz, C. (2012). Denoising of ecg signals based on noise reduction algorithms in emd and wavelet domains. Biomedical Signal Processing and Control, 7(5), 481–489.

    Article  Google Scholar 

  • Martis, R. J., Acharya, U. R., & Min, L. C. (2013). Ecg beat classification using pca, lda, ica and discrete wavelet transform. Biomedical Signal Processing and Control, 8(5), 437–448.

    Article  Google Scholar 

  • Gaci, S. (2014). The use of wavelet-based denoising techniques to enhance the first-arrival picking on seismic traces. IEEE Transactions on Geoscience and Remote Sensing, 52(8), 4558–4563.

    Article  Google Scholar 

  • Ma, J., Plonka, G., & Chauris, H. (2010). A new sparse representation of seismic data using adaptive easy-path wavelet transform. IEEE Geoscience and Remote Sensing Letters, 7(3), 540–544.

    Article  Google Scholar 

  • Villasenor, J. D., Belzer, B., & Liao, J. (1995). Wavelet filter evaluation for image compression. IEEE Transactions on Image Processing, 4(8), 1053–1060.

    Article  Google Scholar 

  • Grgic, M., Ravnjak, M., & Zovko-Cihlar, B. (1999). Filter comparison in wavelet transform of still images. In ISIE’99. Proceedings of the IEEE International Symposium on Industrial Electronics (Cat. No. 99TH8465) (Vol. 1, pp. 105-110). IEEE.

  • Grgic, S., Grgic, M., & Zovko-Cihlar, B. (2001). Performance analysis of image compression using wavelets. IEEE Transactions on Industrial Electronics, 48(3), 682–695.

    Article  Google Scholar 

  • Singh, B. N., & Tiwari, A. K. (2006). Optimal selection of wavelet basis function applied to ecg signal denoising. Digital Signal Processing, 16(3), 275–287.

    Article  Google Scholar 

  • Zhang, Z., Telesford, Q. K., Giusti, C., Lim, K. O., & Bassett, D. S. (2016). Choosing wavelet methods, filters, and lengths for functional brain network construction. PLOS ONE, 11, 1–24.

    Google Scholar 

  • Strang, G., & Nguyen, T. (1997). Wavelets and filter banks, rev (ed ed.). Wellesley, MA: Wellesley-Cambridge Press.

    MATH  Google Scholar 

  • Gnutti, Alessandro (2019). Github repository, https://github.com/AlessandroGnutti/A-wavelet-filter-comparison-on-multiple-datasets-for-signal-comp-and-den, [Online; Accessed 24-September-2019].

  • The usc-sipi image database, http://sipi.usc.edu/database/, [Online; accessed 24-September-2019] (2019).

  • Image compression benchmark, http://imagecompression.info/, [Online; accessed 24-September-2019] (2019).

  • Goldberger, A. L., Amaral, L. A. N., Glass, L., Hausdorff, J. M., Ivanov, P. C., Mark, R. G., et al. (2000). PhysioBank, PhysioToolkit, and PhysioNet: Components of a new research resource for complex physiologic signals. Circulation, 101(23), 215–220.

    Article  Google Scholar 

  • Incorporated research institutions for seismology data, https://www.iris.edu/hq/resource/bb_processing_matlab, [Online; Accessed 24-September-2019] (2019).

  • Boujelbene, R., Jemaa, Y., & Zribi, M. (2019). A comparative study of recent improvements in wavelet-based image coding schemes. Multimedia Tools and Applications, 78, 1649–1683.

    Article  Google Scholar 

  • Bjontegaard, G. (2001). Calculation of average psnr differences between rd-curves, ITU-T VCEG-M33.

  • Vetterli, M., & Herley, C. (1992). Wavelets and filter banks: Theory and design. Trans. Sig. Proc., 40(9), 2207–2232.

    Article  MATH  Google Scholar 

  • Islam, R., Bulbul, F., & Shanta, S. S. (2012). Performance analysis of coiflet-type wavelets for a fingerprint image compression by using wavelet and wavelet packet transform. International Journal of Computer Science and Engineering Survey, 3, 79–87.

    Article  Google Scholar 

  • Soon, Y., Koh, S. N., & Yeo, C. K. (1997, December). Wavelet for speech denoising. In TENCON’97 Brisbane-Australia. In Proceedings of IEEE TENCON’97. IEEE Region 10 annual conference. Speech and image technologies for computing and telecommunications (Cat. No. 97CH36162) (Vol. 2, pp. 479-482). IEEE.

  • Sweldens, W. (1996). The lifting scheme: A custom-design construction of biorthogonal wavelets. Applied and Computational Harmonic Analysis, 3(2), 186–200.

    Article  MathSciNet  MATH  Google Scholar 

  • Averbuch, A. Z., & Zheludev, V. A. (2004). A new family of spline-based biorthogonal wavelet transforms and their application to image compression. IEEE Transactions on Image Processing, 13(7), 993–1007.

    Article  MathSciNet  Google Scholar 

  • Boujelbene, R., Jemaa, Y. B., & Zribi, M. (2016). Toward an optimal B-spline wavelet transform for image compression. In 2016 IEEE/ACS 13th international conference of computer systems and applications (AICCSA) (pp. 1–8). IEEE.

  • Boujelbene, R., Jemaa, Y. B., & Zribi, M. (2017). An efficient codec for image compression based on spline wavelet transform and improved spiht algorithm, in. International Conference on High Performance Computing Simulation (HPCS), 2017, 819–825.

    Article  Google Scholar 

  • Donoho, D. L., & Johnstone, I. M. (1994). Ideal spatial adaptation by wavelet shrinkage. Biometrika, 81(3), 425–455.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Information Engineering, University of Brescia – CNIT, Via Branze 38, 25123, Brescia, Italy

    Alessandro Gnutti, Fabrizio Guerrini, Nicola Adami, Pierangelo Migliorati & Riccardo Leonardi

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  1. Alessandro Gnutti
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  2. Fabrizio Guerrini
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  3. Nicola Adami
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  4. Pierangelo Migliorati
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  5. Riccardo Leonardi
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Correspondence to Alessandro Gnutti.

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Gnutti, A., Guerrini, F., Adami, N. et al. A wavelet filter comparison on multiple datasets for signal compression and denoising. Multidim Syst Sign Process 32, 791–820 (2021). https://doi.org/10.1007/s11045-020-00753-w

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  • DOI: https://doi.org/10.1007/s11045-020-00753-w

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