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Wavelets in Medicine and Biology [Pehme köide]

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Edited by (BEIP/NIH, Bethesda, Maryland, USA), Edited by (BEIP/NIH, Bethesda, Maryland, USA)
  • Formaat: Paperback / softback, 632 pages, kõrgus x laius: 234x156 mm, kaal: 893 g
  • Ilmumisaeg: 18-Dec-2020
  • Kirjastus: Routledge
  • ISBN-10: 0367448599
  • ISBN-13: 9780367448592
Teised raamatud teemal:
Wavelets in Medicine and BiologySuurem pilt
  • Formaat: Paperback / softback, 632 pages, kõrgus x laius: 234x156 mm, kaal: 893 g
  • Ilmumisaeg: 18-Dec-2020
  • Kirjastus: Routledge
  • ISBN-10: 0367448599
  • ISBN-13: 9780367448592
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780367448592.html
Märksõnad:
Considerable attention from the international scientific community is currently focused on the wide ranging applications of wavelets. For the first time, the field's leading experts have come together to produce a complete guide to wavelet transform applications in medicine and biology. Wavelets in Medicine and Biology provides accessible, detailed, and comprehensive guidelines for all those interested in learning about wavelets and their applications to biomedical problems.

Arvustused

"The book is well-produced, and on the whole well-written. It should be useful to research students entering the field, and could be inspiring to mathematics undergraduates interested in real, and indisputably useful, applications of their subject." -David Griffel,The Mathematical Gazette

Part I Wavelet Transform: Theory and Implementation
1 The Wavelet Transform: A Surfing Guide
Akram Aldroubi
1.1 Introduction
3(5)
1.2 Notations
8(3)
1.3 The Continuous Wavelet Transform
11(4)
1.3.1 The Continuous Wavelet Transform of 1-D Signals
11(2)
1.3.2 Multidimensional Wavelet Transform
13(2)
1.4 The Discrete Wavelet Transforms
15(3)
1.4.1 The Dyadic Wavelet Transform
15(2)
1.4.2 The Redundant Discrete Wavelet Transforms
17(1)
1.5 Multiresolutions and Wavelets
18(6)
1.5.1 Multiresolution Approximations of L2
18(2)
1.5.2 Orthogonal MRA-Type Wavelets
20(1)
1.5.3 Semi-Orthogonal MRA-Type Wavelet Bases
21(2)
1.5.4 Bi-Orthogonal MRA-Type Wavelet Bases
23(1)
1.5.5 Local and Global Characterization of Functions in Terms of Their Wavelet Coefficients
23(1)
1.6 Special Bases of Scaling Functions
24(3)
1.6.1 Interpolating Scaling Functions
25(1)
1.6.2 Interpolating Wavelets
26(1)
1.7 Applications and generalizations
27(1)
1.7.1 Applications of the Wavelet Transform
27(1)
1.7.2 Generalizations of the Wavelet Transform
28(1)
1.8 Frame Representations
28(9)
2 A Practical Guide to the Implementation of the Wavelet Transform
Michael Unser
2.1 Introduction
37(2)
2.2 Basic Tools
39(7)
2.2.1 Scaling Functions and Multiresolution Representations
39(3)
2.2.2 Inner Products Via Discrete Convolutions
42(1)
2.2.3 Boundary Conditions
43(3)
2.3 Wavelet Bases (Nonredundant Transform)
46(6)
2.3.1 Fast Dyadic Wavelet Transform
46(2)
2.3.2 Implementation Details
48(4)
2.3.3 Extensions
52(1)
2.4 Dyadic Wavelet Frames
52(5)
2.5 Nondyadic Wavelet Analyses
57(10)
2.5.1 Wavelet Representation
58(2)
2.5.2 Fast Redundant Dyadic Wavelet Transform
60(1)
2.5.3 Fast Redundant Wavelet Transform with Integer Scales
61(1)
2.5.4 Fast Redundant Wavelet Transform (Arbitrary Scales)
62(3)
2.5.5 Fast Redundant Morlet or Gabor Wavelet Transform
65(2)
2.6 Conclusion
67(10)
Part II Wavelets in Medical Imaging and Tomography
3 An Application of Wavelet Shrinkage to Tomography
Eric D. Kolaczyk
3.1 Introduction
77(3)
3.1.1 Tomography
77(1)
3.1.2 Why Wavelets?
78(1)
3.1.3 Wavelet Shrinkage and the Proposed Method
79(1)
3.2 Inversion
80(4)
3.2.1 Direct Data Vs. Indirect Data
80(1)
3.2.2 The Wavelet-Vaguelette Decomposition
81(1)
3.2.3 Efficient Expressions for the Radon Vaguelette Coefficients
82(1)
3.2.4 Calculation of the Radon Vaguelette Coefficient
83(1)
3.3 Denoising Using Wavelet Shrinkage
84(3)
3.3.1 Wavelet Shrinkage with Direct Data
85(1)
3.3.2 Wavelet Shrinkage with Tomographic Data
85(1)
3.3.3 The Proposed Reconstruction Method
86(1)
3.4 A Short Comparative Study
87(2)
3.5 Discussion
89(4)
4 Wavelet Denoising of Functional MRI Data
Michael Hilton
Todd Ogden
David Hattery
Guinevere Eden
Bjorn Jawerth
4.1 Functional MRI and Brain Mapping
93(2)
4.2 Image Acquisition
95(1)
4.3 fMRI Time Series Analysis
96(2)
4.3.1 The Hemodynamic Response Function
97(1)
4.4 Wavelet Denoising of Signals
98(6)
4.4.1 Data Analytic Thresholding
100(4)
4.5 Experimental Results
104(7)
4.5.1 Data Set Descriptions
104(1)
4.5.2 Analysis Technique
105(3)
4.5.3 Denoising Results
108(3)
4.6 Conclusions
111(1)
4.7 Acknowledgment
112(3)
5 Statistical Analysis of Image Differences by Wavelet Decomposition
Urs E. Ruttimann
Michael Unser
Philippe Thevenaz
Chulhee Lee
Daniel Rio
Daniel W. Hommer
5.1 Introduction
115(4)
5.2 Wavelet Transform
119(4)
5.3 Correlation of Wavelet Coefficients
123(5)
5.4 Statistical Tests
128(4)
5.5 Experimental Results
132(7)
5.5.1 Functional Magnetic Resonance Images
132(5)
5.5.2 Positron Emission Tomography Images
137(2)
5.6 Discussion
139(6)
6 Feature Extraction in Digital Mammography
R. A. DeVore
B. Lucier
Z. Yang
6.1 Introduction
145(1)
6.2 Mammograms as Digitized Images
146(3)
6.2.1 Characteristics of Mammographic Images
148(1)
6.3 Compression and Noise Removal
149(3)
6.4 Some Issues in Compression Algorithms
152(1)
6.4.1 Choice of Wavelet Basis
152(1)
6.4.2 Choice of Metric
153(1)
6.4.3 Level of Compression
153(1)
6.5 Algorithms
153(3)
6.6 Examples
156(7)
7 Multiscale Contrast Enhancement and Denoising in Digital Radiographs
Jian Fan
Andrew Laine
7.1 Introduction
163(2)
7.2 One-Dimensional Wavelet Transform
165(5)
7.2.1 General Structure and Channel Characteristics
165(3)
7.2.2 Two Possible Filters
168(2)
7.3 Linear Enhancement and Unsharp Masking
170(3)
7.3.1 Review of Unsharp Masking
170(1)
7.3.2 Inclusion of Unsharp Masking within RDWT Frame-Work
171(2)
7.4 Nonlinear Enhancement
173(3)
7.4.1 Minimum Constraint for an Enhancement Function
173(1)
7.4.2 Filter Selection
173(1)
7.4.3 A Nonlinear Enhancement Function
174(2)
7.5 Combined Denoising and Enhancement
176(4)
7.5.1 Incorporating Wavelet Shrinkage into Enhancement
177(2)
7.5.2 Threshold Estimation for Denoising
179(1)
7.6 Two-Dimensional Extension
180(1)
7.7 Experimental Results and Comparisons
180(3)
7.8 Conclusion
183(4)
7.9 Acknowledgment
187(5)
8 Using Wavelets to Suppress Noise in Biomedical Images
Maurits Malfait
8.1 Introduction
192(1)
8.2 Overview of Wavelet-Based Noise Suppression
193(3)
8.2.1 Wavelet Shrinkage
193(1)
8.2.2 Correlating Coefficients Between Wavelet Levels
194(1)
8.2.3 Smoothness Measure from Wavelet Extrema
195(1)
8.2.4 Example
195(1)
8.3 Introducing an A Priori Model
196(6)
8.3.1 Motivation
196(2)
8.3.2 Basic Idea and Notation
198(1)
8.3.3 Bayesian Method
199(1)
8.3.4 The Conditional Probability
200(1)
8.3.5 The A Priori Probability
201(1)
8.3.6 Coefficient Manipulation
201(1)
8.4 Results for Biomedical Images
202(8)
9 Wavelet Transform and Tomography: Continuous and Discrete Approaches
F. Peyrin
M. Zaim
9.1 Introduction
210(1)
9.2 Basis of Tomography
211(3)
9.2.1 Problem Position
211(1)
9.2.2 Reconstruction Methods: Transform Methods
212(1)
9.2.3 Series Expansion Methods
213(1)
9.3 Continuous Wavelet Decomposition
214(5)
9.3.1 Continuous Wavelet Decomposition of Projections
214(2)
9.3.2 Continuous Wavelet Decomposition of the Image
216(3)
9.4 Discrete Wavelet Decomposition
219(6)
9.4.1 1-D DWT of the Projections
220(3)
9.4.2 2-D Discrete WT of the Image
223(2)
9.5 Conclusion
225(1)
9.5.1 Acknowledgments
225(1)
9.6 Appendix 1
226(5)
10 Wavelets and Local Tomography
Carlos A. Berenstein
David F. Walnut
10.1 Introduction
231(2)
10.2 Background and Notation
233(2)
10.3 Why Wavelets?
235(2)
10.3.1 The Nonlocality of the Radon Transform
235(1)
10.3.2 Wavelets, Vanishing Moments, and A-Tomography
236(1)
10.4 Wavelet Inversion of the Radon Transform
237(12)
10.4.1 The Continuous Wavelet Transform
237(2)
10.4.2 The Semi-Continuous Wavelet Transform
239(2)
10.4.3 The Discrete Wavelet Transform
241(8)
10.5 Wavelet Localization of Radon Transform
249(2)
10.6 Conclusions
251(1)
10.7 Appendix: Proofs of Theorems
251(7)
10.8 Acknowledgments
258(5)
11 Optimal Time-Frequency Projections for Localized Tomography
Tim Olson
11.1 Introduction
263(3)
11.1.1 Historical Notes
263(1)
11.1.2 Prior Work
264(2)
11.1.3 Organization
266(1)
11.2 Algorithmic Goals
266(1)
11.3 Background
266(5)
11.3.1 The Radon Transform
266(4)
11.3.2 Basic Fourier Analysis
270(1)
11.4 Reconstruction Techniques
271(7)
11.4.1 Fourier Reconstruction
271(2)
11.4.2 Filtered Backprojection
273(1)
11.4.3 Nonlocality of the Radon Inversion
273(3)
11.4.4 Visualization via the Sinogram
276(1)
11.4.5 Comparison to Local Tomography
277(1)
11.5 Localization
278(4)
11.5.1 Utilizing Functions with Zero Moments
278(1)
11.5.2 How Many Frequency Windows?
278(1)
11.5.3 High Frequency Computation
279(1)
11.5.4 Low Frequency Computation
280(1)
11.5.5 The Algorithm
281(1)
11.6 Numerical Results
282(1)
11.7 Optimality
283(5)
11.7.1 Minimization of Nonlocal Data
287(1)
11.8 Conclusion
288(1)
11.9 Appendix: Error Analysis
289(3)
11.9.1 Aliasing Error Analysis
289(2)
11.9.2 Truncation Error Analysis
291(1)
11.10 Local Cosine and Sine Bases
292(3)
11.11 Acknowledgments
295(3)
12 Adapted Wavelet Techniques for Encoding Magnetic Resonance Images
Dennis M. Healy Jr.
John B. Weaver
12.1 Introduction
298(1)
12.2 Encoding in Magnetic Resonance Imaging
299(15)
12.2.1 Nuclear Magnetic Resonance
300(3)
12.2.2 Imaging
303(8)
12.2.3 Imaging Time and Signal-to-Noise Ratio
311(3)
12.3 Adapted Waveform Encoding in MRI
314(20)
12.3.1 MRI Encoding with a Basis
315(9)
12.3.2 Figures of Merit in Adapted Waveform Encoding
324(5)
12.3.3 Choosing a Basis for Encoding
329(1)
12.3.4 Implementation of Adapted Waveform Encoding
330(4)
12.4 Reduced Imaging Times
334(12)
12.4.1 Adapted Waveform Encoding with K-L Bases
335(4)
12.4.2 Approximate K-L Bases
339(3)
12.4.3 Approximate Karhunen-Loeve Encoding
342(4)
12.5 Conclusions
346(1)
12.6 Acknowledgments
347(8)
Part III Wavelets and Biomedical Signal Processing
13 Sleep Images Using the Wavelet Transform to Process Polysomnographic Signals
Richard Sartene
Laurent Poupard
Jean-Louis Bernard
Jean-Christophe Wallet
13.1 Introduction
355(2)
13.2 Sleep Polygraphy
357(8)
13.2.1 Signals
357(3)
13.2.2 Sleep Architecture (Figure 13.3)
360(2)
13.2.3 Sleep and Cardiorespiratory Activity [ 5, 9]
362(3)
13.3 The Wavelet Transform--Practical Use
365(5)
13.3.1 Practical Considerations
365(2)
13.3.2 Validation of the Modulation Laws (FM-AM)
367(3)
13.4 Application of the Wavelet Transform
370(6)
13.5 Cardiorespiratory Variations
376(1)
13.6 Interaction Between Two Systems
377(3)
13.7 Conclusion-Perspectives
380(1)
13.8 Acknowledgments
381(2)
14 Estimating the Fractal Exponent of Point Processes in Biological Systems Using Wavelet- and Fourier-Transform Methods
Malvin C. Teich
Conor Heneghan
Steven B. Lowen
Robert G. Turcott
14.1 Introduction
383(5)
14.1.1 Mathematical Descriptions of Stochastic Point Processes
384(1)
14.1.2 Fractal Stochastic Point Processes (FSPPs) Exhibit Scaling
385(1)
14.1.3 The Standard Fractal Renewal Process
386(1)
14.1.4 Examples of Fractal Stochastic Point Processes in Nature
387(1)
14.2 Estimating the Fractal Exponent
388(14)
14.2.1 Coincidence Rate
389(1)
14.2.2 Power Spectral Density
389(1)
14.2.3 Fano Factor
390(2)
14.2.4 Allan Factor
392(1)
14.2.5 Haar-Basis Representation of the Fano and Allan Factors
393(4)
14.2.6 Wavelet-Based Fano and Allan Factors
397(5)
14.3 Comparison of Techniques
402(3)
14.4 Discussion
405(3)
14.5 Conclusion
408(1)
14.6 Acknowledgments
408(5)
15 Point Processes, Long-Range Dependence and Wavelets
Patrice Abry
Patrick Flandrin
15.1 Motivation
413(3)
15.1.1 Long-Range Dependence
413(1)
15.1.2 Point Processes
414(1)
15.1.3 Long-Range Dependent Point Processes
415(1)
15.1.4 Fano Factor
415(1)
15.1.5 Wavelet Analysis
415(1)
15.2 The Standard Fano Factor
416(3)
15.2.1 Some Definitions
416(1)
15.2.2 Poisson Process: Theme and Variations
416(1)
15.2.3 A Long-Dependent Poisson Process
417(1)
15.2.4 Main Limitations
418(1)
15.3 The Wavelet-Based Fano Factor
419(9)
15.3.1 The Multiresolution Point of View
419(3)
15.3.2 Unbiased Estimation of the Long Range-Dependence Parameter: A Key Feature
422(2)
15.3.3 Reduction of the Range of the Dependence: Another Key Feature
424(2)
15.3.4 Fano Factor, Allan Variance and Wavelets
426(1)
15.3.5 Choosing the Number of Vanishing Moments A/"
427(1)
15.4 Practical Issues
428(2)
15.5 Fano Factor and Spectral Estimation
430(2)
15.6 An Example: Spiketrain of an Auditory-Nerve Response
432(2)
15.7 Conclusion
434(5)
16 Continuous Wavelet Transform: ECG Recognition Based on Phase and Modulus Representations and Hidden Markov Models
Lotfi Senhadji
Laurent Thoraval
Guy Carrault
16.1 Introduction
439(2)
16.2 Properties of Square Modulus and Phase
441(4)
16.2.1 Square Modulus Approximation
441(1)
16.2.2 Phase Behavior
442(3)
16.3 Illustration on Signals
445(3)
16.3.1 Results on Simulated Data
445(2)
16.3.2 Results on Real Data
447(1)
16.4 Cardiac Beat Recognition
448(10)
16.5 Results
458(2)
16.6 Conclusion
460(1)
16.7 Appendix
460(5)
17 Interference Canceling in Biomedical Systems: The Mutual Wavelet Packets Approach
Mohsine Karrakchou
Murat Kunt
17.1 Introduction
465(1)
17.2 Pulmonary Capillary Pressure: A Short Review
466(6)
17.2.1 Clinical Relevance
466(2)
17.2.2 In Vivo Estimation: The Occlusion Techniques
468(3)
17.2.3 Limitations in Patients
471(1)
17.3 Basics of Interference Canceling
472(3)
17.3.1 Classical FIR Adaptive Filtering
472(3)
17.4 Multirate Adaptive Filtering
475(2)
17.4.1 Fundamentals of Adaptive Filtering in Subbands
476(1)
17.5 Wavelet Packets
477(3)
17.5.1 The Best Basis Method
478(2)
17.6 Mutual Wavelet Packet Decomposition
480(6)
17.6.1 Introductory Comments
480(1)
17.6.2 The Mutual Wavelet Packets Decomposition
480(2)
17.6.3 Implementation Scheme
482(1)
17.6.4 Algorithmic Complexity
482(2)
17.6.5 Experimental Results
484(2)
17.7 Conclusion
486(7)
18 Frame Signal Processing Applied to Bioelectric Data
John J. Benedetto
18.1 Introduction
493(1)
18.2 Notation
494(1)
18.3 The Theory of Frames
494(2)
18.3.1 Gabor and Wavelet Systems
494(1)
18.3.2 Frames
495(1)
18.4 Frame Multiresolution Analysis (FMRA)
496(2)
18.5 Noise reduction
498(3)
18.6 The Laplacian Method and Gaussian Frames
501(2)
18.7 An Interpretation of Spectral ECoG Data
503(5)
18.8 Appendix
508(5)
19 Diagnosis of Coronary Artery Disease Using Wavelet-Based Neural Networks
Metin Akay
19.1 Introduction
513(3)
19.2 Method
516(3)
19.2.1 Fast Wavelet Transform
516(1)
19.2.2 Fuzzy Min-Max Neural, Networks
517(1)
19.2.3 Patient Analysis
518(1)
19.3 Results
519(3)
19.3.1 Feature Extraction
519(2)
19.3.2 Network Output Representation
521(1)
19.4 Conclusion
522(1)
19.5 Acknowledgment
522(5)
Part IV Wavelets and Mathematical Models in Biology
20 A Nonlinear Squeezing of the Continuous Wavelet Transform Based on Auditory Nerve Models
Ingrid Daubechies
Stephane Maes
20.1 Introduction
527(1)
20.2 Cochlear Filtering
528(1)
20.3 Information Compression
529(2)
20.4 The Modulation Model for Speech
531(2)
20.5 Squeezing the Continuous Wavelet Transform
533(5)
20.6 Short Discussion
538(2)
20.7 Results on Speech Signals
540(4)
20.8 Acknowledgments
544(3)
21 The Application of Wavelet Transforms to Blood Flow Velocimetry
Lora G. Weiss
21.1 Introduction
547(2)
21.2 1-D Measurement Devices
549(2)
21.3 1-D Velocimetry Methods
551(6)
21.3.1 Doppler Methods
552(2)
21.3.2 Time Domain Correlation Methods
554(1)
21.3.3 Limitations
555(2)
21.3.4 Summary of Desirable Signal Characteristics
557(1)
21.4 Wideband/Wavelet Transform Processing
557(8)
21.4.1 Wavelet Transform Processing
557(3)
21.4.2 Parameter Estimation
560(2)
21.4.3 Example
562(3)
21.5 Conclusions
565(1)
21.6 Acknowledgment
566(1)
21.7 Appendix
567(4)
22 Wavelet Models of Event-Related Potentials
Jonathan Raz
Bruce Turetsky
22.1 Introduction
571(2)
22.2 The Single Channel Wavelet Model
573(2)
22.3 Application to Cat Potentials
575(3)
22.4 The Topographic Wavelet Model
578(2)
22.5 Application of Topographic Wavelet Model
580(5)
22.6 Discussion
585(1)
22.7 Acknowledgments
586(4)
23 Macromolecular Structure Computation Based on Energy Function Approximation by Wavelets
Eberhard Schmitt
23.1 Introduction
590(2)
23.2 Domain and Function Decomposition
592(5)
23.2.1 Reduction of the Degrees of Freedom
592(3)
23.2.2 Representation of the Energy Function
595(2)
23.3 Approximation by Wavelets
597(5)
23.3.1 Local Approximation by Cubic B-Spline Wavelets
597(1)
23.3.2 Global Approximation by Tensor Products
598(4)
23.4 Further Applications: Surface Representation
602(1)
23.5 Discussion
603(4)
Index 607
Aldroubi, Akram | Unser, Michael