Multiscale characterization of chronobiological signals based on the discrete wavelet transform

To compensate for the deficiency of conventional frequency-domain or time-domain analysis, this paper presents a multiscale approach to characterize the chronobiological time series (CTS) based on a discrete wavelet transform (DWT). We have shown that the local modulus maxima and zero-crossings of the wavelet coefficients at different scales give a complete characterization of rhythmic activities. We further constructed a tree scheme to represent those interacting activities across scales, Using the bandpass filter property of the DWT in the frequency domain, we also characterized the band-related activities by calculating energy in respective rhythmic bands. Moreover, since there is a fast and easily implemented algorithm for the DWT. This new approach may simplify the signal processing and provide a more efficient and complete study of the temporal-frequency dynamics of the CTS. Preliminary results are presented using the proposed method on the locomotion of mice under altered lighting conditions, verifying its competency for CTS analysis.

[1]  Stéphane Mallat,et al.  Multifrequency channel decompositions of images and wavelet models , 1989, IEEE Trans. Acoust. Speech Signal Process..

[2]  Dennis M. Healy,et al.  Contrast enhancement of medical images using multiscale edge representation , 1994, Defense, Security, and Sensing.

[3]  Stéphane Mallat,et al.  Characterization of Signals from Multiscale Edges , 2011, IEEE Trans. Pattern Anal. Mach. Intell..

[4]  Ingrid Daubechies,et al.  The wavelet transform, time-frequency localization and signal analysis , 1990, IEEE Trans. Inf. Theory.

[5]  John F. Canny,et al.  A Computational Approach to Edge Detection , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  Paul Naitoh,et al.  WinCD : Windows software for complex demodulation , 1995 .

[7]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[8]  J. De Prins,et al.  Data Processing in Chronobiological Studies , 1992 .

[9]  D Marr,et al.  Theory of edge detection , 1979, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[10]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[11]  R. Curtis Graeber,et al.  Rhythmic Aspects of Behavior , 2020 .

[12]  Dennis M. Healy,et al.  Classification of masses in digitized mammograms with features in the wavelet transform domain , 1994, Defense, Security, and Sensing.

[13]  Y. Meyer.  Wavelets and Operators , 1993 .

[14]  Z. Berman.  The Uniqueness Question of Discrete Wavelet Maxima Representation , 1991 .

[15]  B. M. Wu,et al.  Multiscale analysis of activity rhythms of animals , 1995, Proceedings of 17th International Conference of the Engineering in Medicine and Biology Society.

[16]  C. Li,et al.  Detection of ECG characteristic points using wavelet transforms. , 1995, IEEE transactions on bio-medical engineering.

[17]  Dennis M. Healy,et al.  Noise reduction with a multiscale edge representation and perceptual criteria , 1992, [1992] Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis.

[18]  Donald G. Childers,et al.  Modern Spectrum Analysis , 1978 .

[19]  Stanislav B. Kesler.  Modern spectrum analysis, II , 1986 .

[20]  A. Díez-Noguera,et al.  Evolution of rat motor activity circadian rhythm under three different light patterns , 1991, Physiology & Behavior.

[21]  Dennis M. Healy,et al.  Two applications of wavelet transforms in magnetic resonance imaging , 1992, IEEE Trans. Inf. Theory.

[22]  Jacques Beau,et al.  Activity rhythms in mice III: Stability and plasticity of rhythm characteristics in experimental and environmental conditions , 1992, Physiology & Behavior.

[23]  J. Weaver,et al.  Wavelet‐encoded MR imaging , 1992, Magnetic resonance in medicine.

[24]  S.N. Tandon,et al.  Using wavelet transforms for ECG characterization. An on-line digital signal processing system , 1997, IEEE Engineering in Medicine and Biology Magazine.

[25]  F Halberg,et al.  Inferential statistical methods for estimating and comparing cosinor parameters. , 1982, Chronobiologia.

[26]  A. Grossmann,et al.  DECOMPOSITION OF HARDY FUNCTIONS INTO SQUARE INTEGRABLE WAVELETS OF CONSTANT SHAPE , 1984 .

[27]  P.W.F. Poon,et al.  Characterization of the chronobiological signals based on the continuous wavelet transform , 1997, Proceedings of the 19th Annual International Conference of the IEEE Engineering in Medicine and Biology Society. 'Magnificent Milestones and Emerging Opportunities in Medical Engineering' (Cat. No.97CH36136).

[28]  Stéphane Mallat,et al.  Singularity detection and processing with wavelets , 1992, IEEE Trans. Inf. Theory.

[29]  F. K. Lam,et al.  Effect of Cage Size on Ultradian Locomotor Rhythms of Laboratory Mice , 1997, Physiology & Behavior.