Yves Misiti

Wavelets and their applications

Notations. Introduction. Chapter 1. A Guided Tour. Chapter 2. Mathematical Framework. Chapter 3. From Wavelet Bases to the Fast Algorithm. Chapter 4. Wavelet Families. Chapter 5. Finding and Designing a Wavelet. Chapter 6. A Short 1D Illustrated Handbook. Chapter 7. Signal Denoising and Compression. Chapter 8. Image Processing with Wavelets. Chapter 9. An Overview of Applications. Appendix: The EZW Algorithm. Bibliography. Index.

Clustering signals using wavelets

A wavelet-based procedure for clustering signals is proposed. It combines an individual signal preprocessing by wavelet denoising, a dimensionality reduction step by wavelet compression and a classical clustering strategy applied to a suitably chosen set of wavelet coefficients. The ability of wavelets to cope with signals of arbitrary or time-dependent regularity as well as to concentrate signal energy in few large coefficients, offers a useful tool to carry out both significant noise reduction and efficient compression. A simulated example and an electrical dataset are considered to illustrate the value of introducing wavelets for clustering such complex data.