The illustrated wavelet transform handbook. Introductory theory and applications in science, engineering, medicine and finance (Q2832150)

For a review of the first edition (2002) see [Zbl 1081.42025].NEWLINENEWLINEThe second edition, a revised and extended version of the `illustrated wavelet transform handbook' presents in a first part an introduction to wavelets from the user perspective and then in a second part a broad spectrum of applications in different fields in science, engineering, medicine and finance. Chapters 2 and 3 introduce the basics of continuous and discrete wavelet transforms, respectively, without going too much into mathematical details. For the mathematically spoiled reader the presentation becomes somewhat fuzzy, but numerous graphical illustrations can compensate partly this deficit and examples, e.g. for the Haar wavelet transform illustrate the fast algorithm. It can be also noticed that some historical information on wavelets is absent, for example it could be useful to know that wavelets have been introduced by \textit{A. Grossmann} and \textit{J. Morlet} [SIAM J. Math. Anal. 15, 723--736 (1984; Zbl 0578.42007)] and the fast wavelet transform by \textit{S. Mallat} [IEEE Trans. Pattern Anal. Mach. Intell. 11, No.7, 674--693 (1989; Zbl 0709.94650); Trans. Am. Math. Soc. 315, No. 1, 69--87 (1989; Zbl 0686.42018)].NEWLINENEWLINE Applications to fluid mechanics, including turbulence, fluid-structure interaction and geophysical flows are discussed in Chapter 4. Intermittency measures are provided and wavelet-based statistics, e.g. energy spectra, are described. Wavelet thresholding for partitioning turbulent flows into coherent and random contributions is mentioned. Analysis of engineering flows is reviewed and wavelet techniques for computational fluid dynamics, i.e. simulation and analysis, are presented.NEWLINENEWLINE A selection of wavelet techniques for engineering applications, like dynamics and chaos, monitoring of rotating machinery, or characterization of surfaces and fibrous materials, to mention just a selection, is given in Chapter 5.NEWLINENEWLINE Chapter 6 describes numerous medical applications, mostly of electrical or sound signals corresponding to time series, like electrocardiogram, and images obtained by optical ultrasonic or tomographic techniques. Therewith, for example, the heart beat variability can be characterized and abnormalities can be detected. Applications in medical imaging are briefly summarized including magnetic resonance imaging, positron emission tomography, computer tomography, ultra-sonic and optical images. Wavelets are used for exploring the data and getting further insights.NEWLINENEWLINE Chapter 7 presents different applications in a variety of fields, like fractal geometry, finance, geophysics and astronomy. For fractals and multifractals, which are self-similar objects, different wavelet analyses are shown, for example for detecting the Hurst exponent, or the multifractal spectrum. In finance mostly time series of indices or stock market prices are analyzed and wavelet-based correlations are calculated. In geophysics seismic signals are studied and in astronomy some review of applications to both signals and images originating from the solar system or beyond is given. Finally, other areas like quantum mechanics, chemistry, etc. are mentioned. The short appendix lists recommended books and websites.NEWLINENEWLINE The different applications show the interdisciplinary nature of wavelet transforms and their impact in science and technology. The book is well-suited for practical users of wavelets to get an idea of wavelets and applications in different fields, without demanding too much theory and mathematical background. In conclusion, a practical book on wavelets for users of wavelet tools, who do not want to deal with mathematical details and are ready to renounce rigor of mathematics. Many references and numerous examples in different fields give an overview on this rapidly emerging field.