Introduction to Wavelets and Principal Components Analysis

Wavelet analysis found to have a variety of applications. While other transforms such as the DCT may achieve a better compression ratio, their rule of zeroing small coefficients is applied evenly and globally while in wavelet analysis, the rule of zeroing can be applied locally, preserving small coefficients that account for important minute features (such as in fingerprints). Starting with an introduction to wavelet analysis and some related concepts useful for classification the book provides a coverage of the theory and mathematical foundations of wavelets, the Best Basis, the Joint Best Basis, Principal Component Analysis and the Approximate PCA as well as the application of these tools to derive feature vectors for the classification of mammographic images. This book will be useful as a reference text and will benefit both the audience whose interest is at the conceptual level, as it provides a qualitative description of the underlying ideas of wavelet theory and the audience who is interested also in the theory and mathematical foundations of wavelet analysis and its applications.