Wavelets seem to be the most efficient tool in signal denoising and compression. They can be used in an unlimited number of applications in all fields of chemistry where the instrumental signals are the source of information about the studied chemical systems or phenomena, and in all cases where these signals have to be archived. The quality of the instrumental signals determines the quality of answer to the basic analytical questions: how many components are in the studied systems, what are these components like and what are their concentrations? Efficient compression of the signal sets can drastically speed up further processing such as data visualization, modelling (calibration and pattern recognition) and library search. Exploration of the possible applications of wavelets in analytical chemistry has just started and this book will significantly speed up the process.The first part, concentrating on theoretical aspects, is written in a tutorial-like manner, with simple numerical examples. For the reader's convenience, all basic terms are explained in detail and all unique properties of wavelets are pinpointed and compared with the other types of basis function. The second part presents applications of wavelets from many branches of chemistry which will stimulate chemists to further exploration of this exciting subject.
For analytical chemists dealing with any type of spectral data, organic chemists involved in combinatorial chemistry, chemists involved in chemometrics, researchers in artificial intelligence, theoretical chemists and engineers involved in process control.
Table of Contents
Part headings and chapter headings: Preface. Theory. Finding frequencies in signals; the Fourier transform (B. van den Bogaert). When frequencies change in time; towards the wavelet transform (B. van den Bogaert). Fundamentals of wavelet transforms (Y. Mallet et al.). The discrete wavelet transform in practice (O. de Vel et al.). Multiscale methods for denoising and compression (M.N. Nounou, B.R. Bakshi). Wavelet packet transforms and best basis algorithms (Y. Mallet et al.). Joint basis and joint best-basis for data sets (B. Walczak, D.L. Massart). The adaptive wavelet algorithm for designing task specific wavelets (Y. Mallet et al.). Applications. Application of wavelet transform in processing chromatographic data (Foo-tim Chau, A. Kai-man Leung). Application of wavelet transform in electrochemical studies (Foo-tim Chau, A. Kai-man Leung). Applications of wavelet transform in spectroscopic studies (Foo-tim Chau, A. Kai-man Leung). Application of wavelet analysis to physical chemistry (H. Teitelbaum). Wavelet bases for IR library compression, searching and reconstruction (B. Walczak, J.P. Radomski). Application of the discrete wavelet transformation for online detection of transitions in time series (M. Marth). Calibration in wavelet domain (B. Walczak, D.L. Massart). Wavelets in parsimonious functional data analysis models (B.K. Alsberg). Multiscale statistical process control and model-based denoising (B.R. Bakshi). Application of adaptive wavelets in classification and regression (Y. Mallet et al.). Wavelet-based image compression (O. de Vel et al.). Wavelet analysis and processing of 2-D and 3-D analytical images (S.G. Nikolov et al.). Index.