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Wavelets in Chemistry, Volume 22 [Kõva köide]

Edited by (Institute of Chemistry, Silesian University, 9 Szkolna Street, 40-006 Katowice, Poland)
Teised raamatud teemal:
Teised raamatud teemal:
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.
Preface v List Of Contributors xv PART I: THEORY Finding Frequencies in Signals: The Fourier Transform 3(30) B. van den Bogaert Introduction 3(1) The Fourier integral 4(1) Convolution 5(3) Convolution and discrete Fourier 8(1) Polynomial approximation and basis transformation 9(4) The Fourier basis 13(5) Fourier transform: Numerical examples 18(4) Fourier and signal processing 22(6) Apodisation 28(5) When Frequencies Change in Time; Towards the Wavelet Transform 33(24) B. van den Bogaert Introduction 33(2) Short-time Fourier transform 35(5) Towards wavelets 40(13) The wavelet packet transform 53(4) Fundamentals of Wavelet Transforms 57(28) Y. Mallet O. de Vel D. Coomans Introduction 57(2) Continuous wavelet transform 59(4) Inverse wavelet transform 63(2) Discrete wavelet transform 65(1) Multiresolution analysis 65(9) Fast wavelet transform 74(2) Wavelet families and their properties 76(3) Biorthogonal and semiorthogonal wavelet bases 79(6) The Discrete Wavelet Transform in Practice 85(34) O. de Vel Y. Mallet D. Coomans Introduction 85(1) Introduction to matrix theory 85(6) Patterned matrices 86(2) Matrix operations 88(1) Some matrix properties 89(2) Matrix representation of the discrete wavelet transform 91(28) The discrete wavelet transform for infinite signals 91(6) Discrete wavelet transform for signals with finite-length 97(22) Multiscale Methods for Denoising and Compression 119(32) M.N. Nounou B.R. Bakshi Introduction 119(2) Multiscale representation of signals using wavelets 121(2) Characterization of noise 123(3) Autocorrelation function 124(1) Power spectrum 124(2) Wavelet spectrum 126(1) Denoising and compression 126(13) Denoising and compression of data with Gaussian errors 126(10) Filtering of data with non-Gaussian errors 136(3) On-line multiscale filtering 139(9) On-line multiscale filtering of data with Gaussian errors 141(4) OLMS filtering of data with non-Gaussian errors 145(2) Hints for tuning the filter parameters in multiscale filtering and compression 147(1) Conclusions 148(3) Wavelet Packet Transforms and Best Basis Algorithms 151(14) Y. Mallet D. Coomans O. de Vel Introduction 151(1) Wavelet packet transforms 151(4) What do wavelet packet functions look like? 154(1) Best basis algorithm 155(10) Joint Basis and Joint Best-Basis for Data Sets 165(12) B. Walczak D.L. Massart Introduction 165(2) Discrete wavelet transform and joint basis 167(4) Wavelet packet transform and joint best-basis 171(6) The Adaptive Wavelet Algorithm for Designing Ask Specific Wavelets 177(26) Y. Mallet D. Coomans O. de Vel Introduction 177(2) Higher multiplicity wavelets 179(1) m-Band discrete wavelet transform of discrete data 180(5) Filter coefficient conditions 185(1) Factorization of filter coefficient matrices 186(3) Adaptive wavelet algorithm 189(2) Criterion functions 191(3) Introductory examples of the adaptive wavelet algorithm 194(5) Simulated spectra 194(2) Mineral spectra 196(3) Key issues in the implementation of the AWA 199(4) PART II: APPLICATIONS 203(348) Application of Wavelet Transform in Processing Chromatographic Data 205(20) F.-t. Chau A.K.-m. Leung Introduction 205(1) Applications of wavelet transform in chromatographic studies 206(14) Baseline drift correction 207(1) Signal enhancement and noise suppression 208(2) Peak detection and resolution enhancement 210(9) Pattern recognition with combination of wavelet transform and artificial neural networks 219(1) Conclusion 220(5) Application of Wavelet Transform in Electrochemical Studies 225(16) F.-t. Chau A.K.-m. Leung Introduction 225(1) Application of wavelet transform in electrochemical studies 225(11) B-spline wavelet transform in voltammetry 225(8) Other wavelet transform applications in voltammetry 233(3) Conclusion 236(5) Applications of Wavelet Transform in Spectroscopic Studies 241(22) F.-t. Chau A.K.-m. Leung Introduction 241(2) Applications of wavelet transform in infrared spectroscopy 243(7) Novel algorithms for wavelet computation in IR spectroscopy 244(4) Spectral compression with wavelet neural network 248(2) Standardization of IR spectra with wavelet transform 250(1) Applications of wavelet transform in ultraviolet visible spectroscopy 250(4) Pattern recognition with wavelet neural network 251(1) Compression of spectrum with wavelet transform 251(2) Denoising of spectra with wavelet transform 253(1) Application of wavelet transform in mass spectrometry 254(1) Application of wavelet transform in nuclear magnetic resonance spectroscopy 255(1) Application of wavelet transform in photoacoustic spectroscopy 256(1) Conclusion 257(6) Applications of Wavelet Analysis to Physical Chemistry 263(28) H. Teitelbaum Introduction 263(1) Quantum mechanics 264(10) Molecular structure 264(9) Spectroscopy 273(1) Time-series 274(11) Chemical dynamics 274(5) Chemical kinetics 279(3) Fractal structures 282(3) Conclusion 285(6) Wavelet Bases for IR Library Compression, Searching and Reconstruction 291(20) B. Walczak J.P. Radomski Introduction 291(1) Theory 292(5) Wavelet transforms 292(1) Compression of individual signals 292(1) Data set (library) compression 293(1) Compression ratio 294(1) Storage requirements 295(1) Matching criteria 296(1) The data 296(1) Results and discussion 297(11) Principal component analysis applied to IR data compression 297(1) Individual compression of IR spectra in wavelet domain 298(5) Joint basis and joint best-basis approaches to data set compression 303(2) Matching performance 305(3) Conclusions 308(3) Application of the Discrete Wavelet Transformation for Online Detection of Transitions in Time Series 311(12) M. Marth Introduction 311(1) Early transition detection 311(4) Application of the DWT 315(4) Results and conclusions 319(4) Calibration in Wavelet Domain 323(28) B. Walczak D.L. Massart Introduction 323(1) Feature selection coupled with MLR 324(2) Stepwise selection 324(1) Global selection procedures 325(1) Feature selection with latent variable methods 326(7) UVE-PLS 328(3) Feature selection in wavelet domain 331(2) Illustrative example 333(14) Conclusions 347(4) Wavelets in Parsimonious Functional Data Analysis Models 351(60) B.K. Alsberg Introduction 351(1) Functional data analysis 352(9) From vectors to functions 354(1) Spline basis 355(2) Non-linear bases 357(1) Wavelet bases 358(3) Methods for creating parsimonious models 361(14) The simple multiscale approach 362(4) The optimal scale combination (OSC) method 366(1) The masking method 367(2) Genetic algorithms 369(1) The dummy variables approach 369(3) Mutual information 372(1) Selecting large w coefficients 373(2) Regression and classification 375(5) Regression 375(2) Classification 377(3) Example applications 380(31) Regression 380(11) Classification 391(14) Conclusion 405(6) Multiscale Statistical Process Control and Model-Based Denoising 411(46) B.R. Bakshi Introduction 411(1) Wavelets 412(2) General methodology for multiscale analysis, modeling, and optimization 414(1) Multiscale statistical process control 415(7) MSSPC methodology 416(2) MSSPC optimization 418(4) Multiscale denoising with linear steady-state models 422(11) Single-scale model-based denoising 422(3) Multiscale Bayesian data rectification 425(5) Performance of multiscale model-based denoising 430(3) Conclusions 433(4) Application of Adaptive Wavelets in Classification and Regression Y. Mallet D. Coomans O. de Vel Introduction 437(1) Adaptive wavelets and classification analysis 437(11) Review of relevant classification methodologies 437(3) Classification assessment criteria 440(1) Classification criterion functions for the adaptive wavelet algorithm 440(2) Explanation of the data sets 442(2) Results 444(4) Adaptive wavelets and regression analysis 448(9) Review of relevant regression methodologies 448(2) Regression assessment criteria 450(2) Regression criterion functions for the adaptive wavelet algorithm 452(1) Explanation of the data sets 452(1) Results 453(4) Wavelet-Based Image Compression 457(22) O. de Vel D. Coomans Y. Mallet Introduction 457(2) Fundamentals of image compression 459(3) Performance measures for image compression 461(1) Image decorrelation using transform coding 462(11) The Karhunen-Loeve transform (KLT) 462(1) The discrete cosine transform (DCT) 463(2) Wavelet transform coding 465(8) Integrated task-specific wavelets and best-basis search for image compression 473(6) Wavelet Analysis and Processing of 2-D and 3-D Analytical Images 479(72) S.G. Nikolov M. Wolkenstein H. Hutter Introduction 479(3) The 2-D and 3-D wavelet transform 482(5) Mathematical measures 487(1) Image acquisition 487(1) SIMS images 487(1) EPMA images 488(1) Wavelet de-noising of 2-D and 3-D SIMS images 488(14) De-noising via thresholding 488(3) Gaussian and Poisson distributions 491(1) Wavelet de-noising of 2-D SIMS images 491(5) Wavelet de-noising of 3-D SIMS images 496(6) Improvement of image classification by means of de-noising 502(4) Classification 502(1) Results 503(3) Compression of 2-D and 3-D analytical images 506(7) Basics 506(3) Quantisation 509(1) Entropy coding 509(1) Results 509(4) Feature extraction from analytical images 513(13) Edge detection 513(8) Wavelets for texture analysis 521(5) Registration and fusion of analytical images 526(14) Image registration 526(9) Image fusion 535(5) Computation and wavelets 540(2) Conclusions 542(9) Index 551