Wavelets in Chemistry: Walczak: 9780444501110: Book: : eCampus.com

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

List Of Contributors

PART I: THEORY

Finding Frequencies in Signals: The Fourier Transform

(30)

B. van den Bogaert

Introduction

(1)

The Fourier integral

(1)

Convolution

(3)

Convolution and discrete Fourier

(1)

Polynomial approximation and basis transformation

(4)

The Fourier basis

(5)

Fourier transform: Numerical examples

(4)

Fourier and signal processing

(6)

Apodisation

(5)

When Frequencies Change in Time; Towards the Wavelet Transform

(24)

B. van den Bogaert

Introduction

(2)

Short-time Fourier transform

(5)

Towards wavelets

(13)

The wavelet packet transform

(4)

Fundamentals of Wavelet Transforms

(28)

Y. Mallet

O. de Vel

D. Coomans

Introduction

(2)

Continuous wavelet transform

(4)

Inverse wavelet transform

(2)

Discrete wavelet transform

(1)

Multiresolution analysis

(9)

Fast wavelet transform

(2)

Wavelet families and their properties

(3)

Biorthogonal and semiorthogonal wavelet bases

(6)

The Discrete Wavelet Transform in Practice

(34)

O. de Vel

Y. Mallet

D. Coomans

Introduction

(1)

Introduction to matrix theory

(6)

Patterned matrices

(2)

Matrix operations

(1)

Some matrix properties

(2)

Matrix representation of the discrete wavelet transform

(28)

The discrete wavelet transform for infinite signals

(6)

Discrete wavelet transform for signals with finite-length

(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


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