Chemometrics: From Basics to Wavelet TransformISBN: 9780471202424
336 pages
March 2004

This text emphasizes practical applications in chemistry. It employs straightforward language and examples to show the power of wavelet transforms without overwhelming mathematics, reviews other methods, and compares wavelets with other techniques that provide similar capabilities. It uses examples illustrated in MATLAB codes to assist chemists in developing applications, and includes access to a supplementary Web site providing code and data sets for work examples. Wavelet Transformations and Their Applications in Chemistry will prove essential to professionals and students working in analytical chemistry and process chemistry, as well as physical chemistry, spectroscopy, and statistics.
CHAPTER 1: INTRODUCTION.
1.1. Modern Analytical Chemistry.
1.1.1. Developments in Modern Chemistry.
1.1.2. Modern Analytical Chemistry.
1.1.3. Multidimensional Dataset.
1.2. Chemometrics.
1.2.1. Introduction to Chemometrics.
1.2.2. Instrumental Response and Data Processing.
1.2.3. White, Black, and Gray Systems.
1.3. ChemometricsBased Signal Processing Techniques.
1.3.1. Common Methods for Processing Chemical Data.
1.3.2. Wavelets in Chemistry.
1.4. Resources Available on Chemometrics and Wavelet Transform.
1.4.1. Books.
1.4.2. Online Resources.
1.4.3. Mathematics Software.
CHAPTER 2: ONEDIMENSIONAL SIGNAL PROCESSING TECHNIQUES IN CHEMISTRY.
2.1. Digital Smoothing and Filtering Methods.
2.1.1. MovingWindow Average Smoothing Method.
2.1.2. SavitskyGolay Filter.
2.1.3. Kalman Filtering.
2.1.4. Spline Smoothing.
2.2. Transformation Methods of Analytical Signals.
2.2.1. Physical Meaning of the Convolution Algorithm.
2.2.2. Multichannel Advantage in Spectroscopy and Hadamard Transformation.
2.2.3. Fourier Transformation.
2.2.3.1. Discrete Fourier Transformation and Spectral Multiplex Advantage.
2.2.3.2. Fast Fourier Transformation.
2.2.3.3. Fourier Transformation as Applied to Smooth Analytical Signals.
2.2.3.4. Fourier Transformation as Applied to Convolution and Deconvolution.
2.3. Numerical Differentiation.
2.3.1. Simple Difference Method.
2.3.2. MovingWindow Polynomial LeastSquares Fitting Method.
2.4. Data Compression.
2.4.1. Data Compression Based on BSpline Curve Fitting.
2.4.2. Data Compression Based on Fourier Transformation.
2.4.3. Data Compression Based on PrincipalComponent Analysis.
CHAPTER 3: TWODIMENSIONAL SIGNAL PROCESSING TECHNIQUES IN CHEMISTRY.
3.1. General Features of TwoDimensional Data.
3.2. Some Basic Concepts for TwoDimensional Data from Hyphenated Instrumentation.
3.2.1. Chemical Rank and PrincipalComponent Analysis (PCA).
3.2.2. ZeroComponent Regions and Estimation of Noise Level and Background.
3.3. DoubleCentering Technique for Background Correction.
3.4. Congruence Analysis and LeastSquares Fitting.
3.5. Differentiation Methods for TwoDimensional Data.
3.6 Resolution Methods for TwoDimensional Data.
3.6.1. Local PrincipalComponent Analysis and Rankmap.
3.6.2. SelfModeling Curve Resolution and Evolving Resolution Methods.
3.6.2.1. Evolving Factor Analysis (EFA).
3.6.2.2. Window Factor Analysis (WFA).
3.6.2.3. Heuristic Evolving Latent Projections (HELP).
CHAPTER 4: FUNDAMENTALS OF WAVELET TRANSFORM.
4.1. Introduction to Wavelet Transform and Wavelet Packet Transform.
4.1.1. A Simple Example: Haar Wavelet.
4.1.2. Multiresolution Signal Decomposition.
4.1.3. Basic Properties of Wavelet Function.
4.2. Wavelet Function Examples.
4.2.1. Meyer Wavelet.
4.2.2. BSpline (Battle—Lemarié) Wavelets.
4.2.3. Daubechies Wavelets.
4.2.4. Coiflet Functions.
4.3. Fast Wavelet Algorithm and Packet Algorithm.
4.3.1. Fast Wavelet Transform.
4.3.2. Inverse Fast Wavelet Transform.
4.3.3. Finite Discrete Signal Handling with Wavelet Transform.
4.3.4. Packet Wavelet Transform.
4.4. Biorthogonal Wavelet Transform.
4.4.1. Multiresolution Signal Decomposition of Biorthogonal Wavelet.
4.4.2. Biorthogonal Spline Wavelets.
4.4.3. A Computing Example.
4.5. TwoDimensional Wavelet Transform.
4.5.1. Multidimensional Wavelet Analysis.
4.5.2. Implementation of TwoDimensional Wavelet Transform.
CHAPTER 5: APPLICATION OF WAVELET TRANSFORM IN CHEMISTRY.
5.1. Data Compression.
5.1.1. Principle and Algorithm.
5.1.2. Data Compression Using Wavelet Packet Transform.
5.1.3. BestBasis Selection and Criteria for Coefficient Selection.
5.2. Data Denoising and Smoothing.
5.2.1. Denoising.
5.2.2. Smoothing.
5.2.3. Denoising and Smoothing Using Wavelet Packet Transform.
5.2.4. Comparison between Wavelet Transform and Conventional Methods.
5.3. Baseline/Background Removal.
5.3.1. Principle and Algorithm.
5.3.2. Background Removal.
5.3.3. Baseline Correction.
5.3.4. Background Removal Using Continuous Wavelet Transform.
5.3.5. Background Removal of TwoDimensional Signals.
5.4. Resolution Enhancement.
5.4.1. Numerical Differentiation Using Discrete Wavelet Transform.
5.4.2. Numerical Differentiation Using Continuous Wavelet Transform.
5.4.3. Comparison between Wavelet Transform and other Numerical Differentiation Methods.
5.4.4. Resolution Enhancement.
5.4.5. Resolution Enhancement by Using Wavelet Packet Transform.
5.4.6. Comparison between Wavelet Transform and Fast Fourier Transform for Resolution Enhancement.
5.5. Combined Techniques.
5.5.1. Combined Method for Regression and Calibration.
5.5.2. Combined Method for Classification and Pattern Recognition.
5.5.3. Combined Method of Wavelet Transform and Chemical Factor Analysis.
5.5.4. Wavelet Neural Network.
5.6. An Overview of the Applications in Chemistry.
5.6.1. Flow Injection Analysis.
5.6.2. Chromatography and Capillary Electrophoresis.
5.6.3. Spectroscopy.
5.6.4. Electrochemistry.
5.6.5. Mass Spectrometry.
5.6.6. Chemical Physics and Quantum Chemistry.
5.6.7. Conclusion.
APPENDIX VECTOR AND MATRIX OPERATIONS AND ELEMENTARY MATLAB.
A.1. Elementary Knowledge in Linear Algebra.
A.1.1. Vectors and Matrices in Analytical Chemistry.
A.1.2. Column and Row Vectors.
A.1.3. Addition and Subtraction of Vectors.
A.1.4. Vector Direction and Length.
A.1.5. Scalar Multiplication of Vectors.
A.1.6. Inner and Outer Products between Vectors.
A.1.7. The Matrix and Its Operations.
A.1.8. Matrix Addition and Subtraction.
A.1.9. Matrix Multiplication.
A.1.10. Zero Matrix and Identity Matrix.
A.1.11. Transpose of a Matrix.
A.1.12. Determinant of a Matrix.
A.1.13. Inverse of a Matrix.
A.1.14. Orthogonal Matrix.
A.1.15. Trace of a Square Matrix.
A.1.16. Rank of a Matrix.
A.1.17. Eigenvalues and Eigenvectors of a Matrix.
A.1.18. SingularValue Decomposition.
A.1.19. Generalized Inverse.
A.1.20. Derivative of a Matrix.
A.1.21. Derivative of a Function with Vector as Variable.
A.2. Elementary Knowledge of MATLAB.
A.2.1. Matrix Construction.
A.2.2. Matrix Manipulation.
A.2.3. Basic Mathematical Functions.
A.2.4. Methods for Generating Vectors and Matrices.
A.2.5. Matrix Subscript System.
A.2.6. Matrix Decomposition.
A.2.6.1. SingularValue Decomposition (SVD).
A.2.6.2. Eigenvalues and Eigenvectors (eig).
A.2.7. Graphic Functions 288
INDEX.
YIZENG LIANG, PhD, is a Professor in the College of Chemistry and Chemical Engineering at Central South University, China.
JUNBIN GAO, PhD, is a Professor in the Department of Mathematics at Huazhong University of Science and Technology. He is currently visiting the University of Southhampton.
XUEGUANG SHAO, PhD, is a Professor at the University of Science and Technology in China.
"...quite useful for persons who apply signal processing methods in chemistry." (Technometrics, May 2005)
"…my overall impression of the text is favorable…I would recommend this book to chemists who are interested in using wavelets in their research and to faculty…" (Journal of the American Chemical Society, February 23, 2005)
"I recommend this book to chemists who are interested in using wavelets in their research and to faculty who would like to teach graduate students about signal processing..." (Analytical Chemistry, February 1, 2005)
"The presentation of information makes it easy for reader to find the relevant information. The text is wellwritten and understandable." (ESTREAMS, October 2004)