Book contents
- Frontmatter
- Contents
- Prologue
- 1 Warm-up: the 1-D continuous wavelet transform
- 2 The 2-D continuous wavelet transform
- 3 Some 2-D wavelets and their performance
- 4 Applications of the 2-D CWT. I: image processing
- 5 Applications of the 2-D CWT. II: physical applications
- 6 Matrix geometry of wavelet analysis. I
- 7 Matrix geometry of wavelet analysis. II
- 8 Minimal uncertainty and Wigner transforms
- 9 Higher-dimensional wavelets
- 10 Spatio-temporal wavelets and motion estimation
- 11 Beyond wavelets
- Epilogue
- Appendix: Some elements of group theory
- References
- Index
5 - Applications of the 2-D CWT. II: physical applications
Published online by Cambridge University Press: 19 August 2009
- Frontmatter
- Contents
- Prologue
- 1 Warm-up: the 1-D continuous wavelet transform
- 2 The 2-D continuous wavelet transform
- 3 Some 2-D wavelets and their performance
- 4 Applications of the 2-D CWT. I: image processing
- 5 Applications of the 2-D CWT. II: physical applications
- 6 Matrix geometry of wavelet analysis. I
- 7 Matrix geometry of wavelet analysis. II
- 8 Minimal uncertainty and Wigner transforms
- 9 Higher-dimensional wavelets
- 10 Spatio-temporal wavelets and motion estimation
- 11 Beyond wavelets
- Epilogue
- Appendix: Some elements of group theory
- References
- Index
Summary
In the previous chapter, we have discussed a number of applications of the 2-D CWT that belong essentially to the realm of image processing. Besides these, however, there are plenty of applications to genuine physical problems, in such diverse fields as astrophysics, geophysics, fluid dynamics or fractal analysis. Here the CWT appears as a new analysis tool, that often proves more efficient than traditional methods, which in fact rarely go beyond standard Fourier analysis. We will review some of these applications in the present chapter, without pretention of exhaustivity, of course. Our treatment will often be sketchy, but we have tried to provide always full references to the original papers.
Astronomy and astrophysics
Wavelets and astronomical images
Astronomical imaging has distinct characteristics. First, the Universe has a marked hierarchical structure, almost fractal. Nearby stars, galaxies, quasars, galaxy clusters and superclusters have very different sizes and live at very different distances, which means that the scale variable is essential and a multiscale analysis is in order, instead of the usual Fourier methods. This suggests wavelet analysis. Now, the main problem is that of detecting particular features, relations, groupings, etc., in images, which leads us to prefer the continuous WT over the discrete WT. Finally, there is in general no privileged direction, nor particular oriented features, in astrophysical images.
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- Two-Dimensional Wavelets and their Relatives , pp. 175 - 213Publisher: Cambridge University PressPrint publication year: 2004