×

Explicit Haar-Schauder multiwavelet filters and algorithms. II: Relative entropy-based estimation for optimal modeling of biomedical signals. (English) Zbl 1425.92122

Summary: Biomedical signal/image processing and analysis are always fascinating tasks in scientific researches, both theoretical and practical. One of the powerful tools in such topics is wavelet theory which has been proved to be challenging since its discovery. One of the best measures of the optimality of reconstruction of signals/images is the well-known Shannon’s entropy. In wavelet theory, this is very well known and researchers are familiar with it. In the present work, a step forward is proposed based on more general wavelet tools. New approach is proposed for the reconstruction of signals/images provided with multiwavelets Shannon-type entropy to evaluate the order/disorder of the reconstructed signals/images. Efficiency and accuracy of the approach is confirmed by a simulation study on several models such as ECG, EEG and DNA/protein signals. For Part I see [Zbl 07115628].

MSC:

92C55 Biomedical imaging and signal processing
94A17 Measures of information, entropy
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Arfaoui, S., Rezgui, I. and Ben Mabrouk, A., Wavelet Analysis on the Sphere, Spheroidal Wavelets (Degruyter, 2017). · Zbl 1369.42026
[2] Attakitmongcol, K., Hardin, D. P. and Wilkes, D. M., Multiwavelet prefilters — part II: Optimal orthogonal prefilters, IEEE Trans. Image Process.10(10) (2001) 1476-1487. · Zbl 1028.94007
[3] A. Ben Mabrouk and M. M. Ibrahim Mahmoud, Multifractal study of some biological series, the case of proteins, IWSSIP, 2013.
[4] Ben Mabrouk, A., Rabbouch, B. and Saadaoui, F., A wavelet based methodology for predicting transmembrane segments. Poster Session, Int. Conf. Engineering Sciences for Biology and Medecine, 1-3 May 2015, Monastir, Tunisia, .
[5] Bhatnagar, S. and Jain, R. C., Comparative analysis and applications of Multi wavelet transform in image Denoising, Int. J. Cybernet. Inf.4(2) (2015) 157-165.
[6] Bianca, C., Pappalardo, F., Pennisi, M. and Ragusa, M. A., Persistence analysis in a Kolmogorov-type model for cancer-immune system competition, AIP Conf. Proc.1558 (2013) 1797-1800, https://doi.org/10.1063/1.4825874.
[7] Bin, Y. and Zhang, Y., A simple method for predicting transmembrane proteins based on wavelet transform, Int. J. Biol. Sci.9(1) (2013) 22-33.
[8] Bin, Y. and Zhang, Y., On the prediction of transmembrane helical segments in membrane proteins, World Acad. Sci. Eng. Technol.37 (2010) 554-557.
[9] C. R. Brazile, Multivariate multiresolution multiwevelets, Thesis in Mathematics. Texas Tech University (2009).
[10] Bulusu, K. V. and Plesniak, M. W., Shannon entropy-based wavelet transform method for autonomous coherent structure identification in fluid flow field data, Entropy17 (2015) 6617-6642.
[11] Coifman, R. R. and Wickerhauser, M. V., Entropy-based algorithms for best basis selection, IEEE Trans. Inf. Theory38 (1992) 713-718. · Zbl 0849.94005
[12] Cole, S. R. and Voytek, B., Brain oscillations and the importance of waveform shape, Trends Cogn. Sci.21(2) (2017) 137-149.
[13] Fischer, P., Multiresolution analysis for 2D turbulence Part 1: Wavelets vs cosince packets, a comparative study, Discr. Contin. Dyn. Syst. B5 (2005) 659-686. · Zbl 1140.76350
[14] Guariglia, E., Entropy and fractal antennas, Entropy18(3) (2016) 1-17.
[15] Guariglia, E., Spectral analysis of the Weierstrass-Mandelbrot function, 2nd Int. Multidisciplinary Conf. Computer and Energy Science, SpliTech 2017, Article number 8019284, ISBN: 978-953290071-2, (2017), pp. 266-271.
[16] Guariglia, E., Harmonic Sierpinski Gasket and applications, Entropy20(9) (2018) 714.
[17] Guido, R. C., Barbon, S. Jr, Vieira, L. S.et al., Introduction to the discrete shapelet transform and a new paradigm: Joint time-frequency-shape analysis, in Proc. IEEE Int. Symp. Circuits and Systems (IEEE ISCAS, 2008), Seattle, WA, USA, , Vol. 1, 2008, pp. 2893-2896.
[18] Hardin, D. P. and Roach, D. W., Multiwavelet Prefilters I: Orthogonal Prefilters Preserving Approximation Order p-2, IEEE Trans. Circuits Syst.-II: Analog and Digital Signal Processing45(8) (1998) 1106-1112. · Zbl 0997.94505
[19] Ibrahim Mahmoud, M. M., Ben Mabrouk, A. and Hashim, M. A., Wavelet multifractal models for transmembrane proteins series, Int. J. Wavelets, Multiresolut. Inf. Process.14(6) (2016) 36. · Zbl 1353.42034
[20] M. Jallouli, M. Zemni, A. Ben Mabrouk and M. A. Mahjoub, Towards recursive spherical harmonics issued Bi-Filters: Part I: Theoretical framework, Soft Comput., in press 2018, 23 p. · Zbl 1430.94043
[21] Keinert, F., Wavelets and Multiwavelets (Chapman and Hall/CRC, 2004). · Zbl 1058.65150
[22] Kitti, A., Multiwavelet Prefilters — Part II: Optimal Orthogonal prefilters, IEEE Transactions Image Process.10(10) (2001) 1476-1487. · Zbl 1028.94007
[23] Kolmogorov, A. N., On the Shannon theory of information transmission in the case of continuous signals, IRE Trans. Inf. Theory2 (1956) 102-108.
[24] Kyte, J. and Doolittle, R. F., A simple method for displaying the hydrophathic character of a protein, J. Mol. Biol.157 (1982) 105-132.
[25] Labat, D., Recent advances in wavelet analyses: Part 1, A review of concepts, J. Hydrol.314 (2005) 275-288.
[26] Mallat, S., A Wavelet Tour of Signal Processing, 3rd edn. (Academic Press, 2008). · Zbl 0998.94510
[27] Nicolis, O. and Mateu, J., 2D Anisotropic wavelet entropy with an application to earthquakes in Chile, Entropy17 (2015) 4155-4172.
[28] V. Perrier, Les ondelettes, un outil gnrique pour le traitement du signal et la simulation, Colloque MFI, Juin 2012.
[29] Rosso, O., Blanco, S., Yordanova, J., Kolev, V., Figliola, A., Schrrmann, M. and Basar, E., Wavelet entropy: A new tool for analysis of short durationB electrical signals, J. Neurosci. Methods105(1) (2001) 65-75.
[30] Ruppert-Felsot, J. E., Praud, O., Sharon, E. and Swinney, H. L., Extraction of coherent structures in a rotating turbulent flow experiment, Phys. Rev. E72 (2005) 17.
[31] Shannon, C., A mathematical theory of communication, Bell Syst. Tech. J.27 (1948) 379-423. · Zbl 1154.94303
[32] Singh, R. and Khare, A., Fusion of multimodal medical images using daubechies complex wavelet transform — A multiresolution approach, Inf. Fusion19 (2014) 49-60.
[33] Stankovic, R. S. and Falkowski, B. J., The Haar wavelet transform: Its status and achievements, Comput. Electr. Eng.29 (2003) 25-44. · Zbl 1059.65132
[34] Taubin, G., A signal processing approach to fair surface design in SIGGRAPH95: Proc. 22nd Annual Conf. Computer Graphics and Interactive Techniques, New York, NY, USA, , (1995), pp. 35-58.
[35] Von Hejine, G., Membrane protein structure prediction, Hydrophobicity analysis and the positive-inside rule, J. Mol. Biol.225(2) (1992) 487-494.
[36] Wang, Z., Wan, F., Wong, C. M. and Zhang, L., Adaptive Fourier decomposition based ECG denoising, Comput. Biol. Medicine77(1) (2016) 195-205.
[37] M. Zemni, M. Jallouli, A. Ben Mabrouk and M. A. Mahjoub, Towards new multiwavelets: Associated filters and algorithms. Part I: Theoretical framework, Soft Comput., Submitted in revised form, 2018, 20 pages. · Zbl 1430.94043
[38] Zhang, J. K., Davidson, T. N., Luo, Z. Q. and Wong, K. M., Design of interpolating biorthogonal multiwavelet systems with compact support, Appl. Comput. Harmon. Anal.11 (2001) 420-438. · Zbl 1010.42018
[39] Zheng, S. and Ouyang, Z., Stability of solitary traveling waves of moderate amplitude with non-zero boundary, Bound. Value Probl., Article Number77, (2017). · Zbl 1366.35154
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.