Skip to main content
Article thumbnail
Location of Repository

Wavelet analysis of temporal data

By David Alexander Goodwin


This thesis considers the application of wavelets to problems involving multiple series\ud of temporal data. Wavelets have proven to be highly effective at extracting frequency\ud information from data. Their multi-scale nature enables the efficient description of both\ud transient and long-term signals. Furthermore, only a small number of wavelet coefficients\ud are needed to describe complicated signals and the wavelet transform is computationally\ud efficient.\ud \ud In problems where frequency properties are known to be important, it is proposed that\ud a modelling approach which attempts to explain the response in terms of a multi-scale\ud wavelet representation of the explanatory series will be an improvement on standard\ud regression techniques. The problem with classical regression is that differing frequency\ud characteristics are not exploited and make the estimates of the model parameters less\ud stable. The proposed modelling method is presented with application to examples from\ud seismology and tomography.\ud \ud In the first part of the thesis, we investigate the use of the non-decimated wavelet transform\ud in the modelling of data produced from a simulated seismology study. The fact that elastic\ud waves travel with different velocities in different rock types is exploited and wavelet\ud models are proposed to avoid the complication of predictions being unstable to small\ud changes in the input data, that is an inverse problem.\ud \ud The second part of the thesis uses the non-decimated wavelet transform to model electrical\ud tomographic data, with the aim of process control. In industrial applications of electrical\ud tomography, multiple voltages are recorded between electrodes attached to the boundary\ud of, for example, a pipe. The usual first step of the analysis is then to reconstruct the\ud conductivity distribution within the pipe. The most commonly used approaches again lead\ud to inverse problems, and wavelet models are again used here to overcome this difficulty.\ud We conclude by developing the non-decimated multi-wavelet transform for use in the\ud \ud modelling processes and investigate the improvements over scalar wavelets

Publisher: Statistics (Leeds)
Year: 2008
OAI identifier:

Suggested articles


  1. (2001). A MATLAB package for the EIDORS project to reconstruct two-dimensional EIT images. Physiological Measurement,
  2. (1995). Adapting to unknown smoothness via wavelet shrinkage.
  3. (2002). An introduction to seismology, earthquakes and earth structure.
  4. (2003). Application of wavelet modulus maxima for microarray spot recognition.
  5. (1997). Correlationpatternsincharacteristicsofspatiallyvariableseismic ground motions. Earthquake engineering and structural dynamics,
  6. (1999). Electrode models for electric current computed tomography.
  7. (1995). Electronic filter design handbook (3rd Edition).
  8. (1981). Estimation of the mean of a multivariate normal distribution.
  9. (2005). Extending the Linear Model with R.
  10. (2007). Foundation for Statistical Computing,
  11. (1996). Fourier Analysis.
  12. (1995). Frequency-time decomposition of seismic data using wavelet-based methods.
  13. (1999). G.Strang, P.Topiwala, andC.Heil. Theapplicationofmultiwavelet filter banks to image processing.
  14. (2007). Geophysical Signal Analysis.
  15. (1996). GOES-8 x-ray sensor variance stabilization using the multiscale data-driven haar-fisz transform.
  16. (1994). Ideal spatial adaptation by wavelet shrinkage.
  17. (2004). Industrial process tomography progress. In
  18. (1996). Intertwining multiresolution analyses and the construction of piecewise-polynomial wavelets.
  19. (2004). Markov chain monte carlo techniques and spatial-temporal modelling for medical EIT. Physiological Measurements,
  20. (1997). Methods for statistical data analysis of multivariate observations (2nd Edition).
  21. (1992). Metropolis methods, gaussian proposals, and antithetic variables. Lecure notes in Statistics,
  22. (2002). Modern Applied Statistics with S.
  23. (2001). Multidimensional Scaling.
  24. (2005). Multivariate Statistical Methods: A Primer. Chapman & Hall/CRC,
  25. (2006). Nondestructive dynamic process monitoring using electrical capacitance tomography.
  26. (1930). On the theory of filter amplifiers.
  27. (1991). Ondelettes sur l’intervalle.
  28. (1988). Orthonormal bases of compactly supported wavelets.
  29. (2002). Posterior probability intervals for wavelet thresholding.
  30. (2003). Process tomography and particle tracking: Research tool and commercial diagnostic tool.
  31. (1981). Robust Statistics.
  32. (1999). Seismic data analysis based on fuzzy clustering.
  33. (1995). Short wavelets and matrix dilation equations.
  34. (1981). Spectral Analysis and Time Series.
  35. (1999). Statistical Modeling by Wavelets.
  36. (2006). Surfing the brain — an overiew of waveletbased techniques for fMRI data analysis.
  37. (1992). Ten Lectures on Wavelets
  38. (1998). The discrete multiple wavelet transform and thresholding methods.
  39. (1994). The discrete wavelet transform in s.
  40. (1995). The stationary wavelet transform and some statistical applications.
  41. (1976). Time Series Analysis: Forecasting and Control. Holden Day,
  42. (1993). Tomographic techniques for characterising particulate processes.
  43. (1996). Unexpected spatial patterns in exponential family auto models. Graphical models and image processing,
  44. (2000). Wavelet analysis and its statistical applications.
  45. (2005). Wavelet image denoising using localised thresholding operators.
  46. (2000). Wavelet methods for time series analysis.
  47. (1998). Wavelet thresholding via a bayesian approach.
  48. (2004). Wavelets and Multiwavelets. Chapman and Hall /
  49. (1992). Wavelets and Operators.

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.