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.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
Tax calculation will be finalised during checkout.
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.
Again, refer to Gnutti (2019) for the HD high precision image set performance.
Daubechies, I. (1992). Ten Lectures on Wavelets. Philadelphia, PA, USA: Society for Industrial and Applied Mathematics.
Vetterli, M., & Kovačevic, J. (1995). Wavelets and Subband Coding. Upper Saddle River, NJ, USA: Prentice-Hall Inc.
Mallat, S. (1999). A wavelet tour of signal processing. New York: Elsevier.
Ohm, J. (1994). Three-dimensional subband coding with motion compensation. IEEE Transactions on Image Processing, 3(5), 559–571.
Lewis, A. S., & Knowles, G. (1992). Image compression using the 2-d wavelet transform. IEEE Transactions on Image Processing, 1(2), 244–250.
Antonini, M., Barlaud, M., Mathieu, P., & Daubechies, I. (1992). Image coding using wavelet transform. IEEE Transactions on Image Processing, 1(2), 205–220.
DeVore, R. A., Jawerth, B., & Lucier, B. J. (1992). Image compression through wavelet transform coding. IEEE Transactions on Information Theory, 38(2), 719–746.
Usevitch, B. E. (2001). A tutorial on modern lossy wavelet image compression: Foundations of jpeg 2000. IEEE Signal Processing Magazine, 18(5), 22–35.
Shapiro, J. M. (1993). Embedded image coding using zerotrees of wavelet coefficients. IEEE Transactions on Signal Processing, 41(12), 3445–3462.
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.
Lazzaroni, F., Leonardi, R., & Signoroni, A. (2003). High-performance embedded morphological wavelet coding. IEEE Signal Processing Letters, 10(10), 293–295.
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.
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.
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.
Bruylants, T., Munteanu, A., & Schelkens, P. (2015). Wavelet based volumetric medical image compression. Signal Processing: Image Communication, 31, 112–133.
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.
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.
Luisier, F., Vonesch, C., Blu, T., & Unser, M. (2010). Fast interscale wavelet denoising of poisson-corrupted images. Signal Processing, 90(2), 415–427.
Luisier, F., Blu, T., & Unser, M. (2011). Image denoising in mixed poisson-gaussian noise. IEEE Transactions on Image Processing, 20(3), 696–708.
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.
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.
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.
Demirel, H., & Anbarjafari, G. (2011). Image resolution enhancement by using discrete and stationary wavelet decomposition. IEEE Transactions on Image Processing, 20(5), 1458–1460.
Demirel, H., & Anbarjafari, G. (2011). Discrete wavelet transform-based satellite image resolution enhancement. IEEE Transactions on Geoscience and Remote Sensing, 49(6), 1997–2004.
Singh, R., & Khare, A. (2014). Fusion of multimodal medical images using daubechies complex wavelet transform - A multiresolution approach. Information Fusion, 19, 49–60.
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.
Li, S., Yang, B., & Hu, J. (2011). Performance comparison of different multi-resolution transforms for image fusion. Information Fusion, 12(2), 74–84.
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.
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.
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.
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.
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.
Villasenor, J. D., Belzer, B., & Liao, J. (1995). Wavelet filter evaluation for image compression. IEEE Transactions on Image Processing, 4(8), 1053–1060.
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.
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.
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.
Strang, G., & Nguyen, T. (1997). Wavelets and filter banks, rev (ed ed.). Wellesley, MA: Wellesley-Cambridge Press.
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.
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.
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.
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.
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.
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.
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.
Donoho, D. L., & Johnstone, I. M. (1994). Ideal spatial adaptation by wavelet shrinkage. Biometrika, 81(3), 425–455.
Conflicts of interest
The authors declare that they have no conflict of interest.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Gnutti, A., Guerrini, F., Adami, N. et al. A wavelet filter comparison on multiple datasets for signal compression and denoising. Multidim Syst Sign Process (2021). https://doi.org/10.1007/s11045-020-00753-w
- Sub-band coding
- Discrete wavelet transform
- Wavelet filter comparison
- Multiresolution analysis