UID:
almahu_9947367266502882
Umfang:
1 online resource (321 p.)
Ausgabe:
1st ed.
ISBN:
1-281-18669-4
,
9786611186692
,
0-08-052780-9
,
1-4356-3199-4
Serie:
Studies in computational mathematics ; 10
Inhalt:
""Beyond Wavelets"" presents state-of-the-art theories, methods, algorithms, and applications of mathematical extensions for classical wavelet analysis. Wavelets, introduced 20 years ago byMorlet and Grossmann and developed very rapidly during the 1980's and 1990's, has created a common link between computational mathematics and other disciplines of science and engineering.Classical wavelets have provided effective and efficient mathematical tools for time-frequency analysis which enhances and replaces the Fourier approach.However, with the current advances in science and techn
Anmerkung:
Description based upon print version of record.
,
Cover; Preface; Contents; Chapter 1. Digital Ridgelet Transform based on True Ridge Functions; 1.1 Introduction; 1.2 Digital Ridgelets; 1.3 Relation to Fast Slant Stack; 1.4 Structural Analogies; 1.5 Example: HalfDome; 1.6 Sparsity of the Frame Kernel; 1.7 Comparisons; 1.8 Discussion; References; Chapter 2. Digital Implementation of Ridgelet Packets; 2.1 Introduction; 2.2 Fourier Preliminaries; 2.3 Radon Preliminaries; 2.4 The Ridgelet Construction, and its Properties; 2.5 Ridgelet Packet Construction; 2.6 Implementation on Digital Data; 2.7 Adaptation; 2.8 Discussion; References
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Chapter 3. Brushlets: Steerable Wavelet Packets3.1 Introduction; 3.2 Biorthogonal windowed Fourier bases; 3.3 Choice of the bell function; 3.4 Biorthogonal brushlet bases; 3.5 Conclusion; References; Chapter 4. Contourlets; 4.1 Introduction and Motivation; 4.2 Representing 2-D Piecewise Smooth Functions; 4.3 Pyramidal Directional Filter Bank; 4.4 Multiresolution Analysis; 4.5 Numerical Experiments; 4.6 Conclusion; References; Chapter 5. ENO-wavelet Transforms and Some Applications; 5.1 Introduction; 5.2 The ENO-Wavelet Algorithm; 5.3 Theory: Error Bound and Stability; 5.4 Application
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ReferencesChapter 6. A Mechanical Image Model for Bayesian Tomographic Reconstruction; 6.1 Introduction and Background; 6.2 Materials and Methods; 6.3 Results and Discussion; References; Chapter 7. Recent Development of Spline Wavelet Frames with Compact Support; 7.1 Introduction; 7.2 Characterization of Wavelet Spline Frames; 7.3 Wavelet Frames of Splines with Multiple Knots; 7.4 The Common Link: Approximate Duals; 7.5 Tight Spline Frames with Non-uniform Knots; References; Chapter 8. Afiine, Quasi-Affine and Co-Affine Wavelets; 8.1 Introduction
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8.2 Frames and the three systems X(Ψ), X*(Ψ), and X(Ψ)References; Chapter 9. Sparsity vs. Statistical Independence in Adaptive Signal Representations: A Case Study of the Spike Process; 9.1 Introduction; 9.2 Notation and Terminology; 9.3 Sparsity vs. Statistical Independence; 9.4 Two-Dimensional Counterexample; 9.5 The Spike Process; 9.6 Proofs of Propositions and Theorems; 9.7 Discussion; 9.8 Appendices; References; Chapter 10. Nonuniform Filter Banks: New Results and Open Problems; 10.1 Introduction; 10.2 Background: Equivalent Uniform FBs; PR Equations
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10.3 Problem Statement, and Unconstrained FBs10.4 Tree Structures; 10.5 Delay-chains; 10.6 The Class of Rational FBs; 10.7 Conditions Based on Reductions to Tree Structures; 10.8 Summary and Comparison of Necessary Conditions; 10.9 Concluding Remarks; 10.10 Appendices; References; Index
,
English
Weitere Ausg.:
ISBN 0-12-743273-6
Sprache:
Englisch
