The Maximum Entropy Method - Wu, Nailong

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Résumé :
BThe Maximum Entropy Method /B(MEM) has its roots in the Principle of Maximum Entropy introduced by Jaynes into the field of statistical mechanics almost 40 years ago. This principle has since been adopted in many areas of science and technology, such as spectral analysis and image restoration. This monograph consists of five chapters and two appendices. The first three chapters are devoted to MEM and its applications in spectral analysis and image restoration, including algrorithms in practical use. Chapter 4 is concerned with experimental and theoretical analysis and comparison of the basic ideas, and properties and applications of MEM. Chapter 5 presents MEM in mathematics and physics. The appendices provide relevant details of cepstral analysis and image restoration.

Sommaire:
1. Introduction.- 1.1 What is the Maximum Entropy Method.- 1.2 Definition of Entropy.- 1.3 Rationale of the Maximum Entropy Method.- 1.4 Present and Future Research.- 2. Maximum Entropy Method MEM1 and Its Application in Spectral Analysis.- 2.1 Definition and Expressions of Entropy H1.- 2.2 Formulation and Solution.- 2.3 Equivalents and Signal Model.- 2.4 Algorithms and Numerical Example (Given ACF).- 2.5 Algorithms and Numerical Example (Given Time Series).- 2.6 Order Selection.- 3. Maximum Entropy Method MEM2 and Its Application in Image Restoration.- 3.1 Definition and Expressions of Entropy H2.- 3.2 Formulation and Implicit Solution.- 3.3 Explicit Solution.- 3.4 Equivalents and Signal Model.- 3.5 R - ? Procedure.- 3.6 Algorithms and Numerical Examples (I).- 3.7 Algorithms and Numerical Examples (II).- 3.8 Algorithms and Numerical Examples (III).- 4. Analysis and Comparison of the Maximum Entropy Method.- 4.1 Generalized MEM.- 4.2 Expressions of Entropy.- 4.3 Solution's Properties.- 4.4 Resolution Enhancement and Data Extension (Experimental Results).- 4.5 Resolution Enhancement and Data Extension (Theoretical Analysis).- 4.6 Peak Location and Relative Power Estimation (Experimental Results).- 4.7 Peak Location and Relative Power Estimation (Theoretical Analysis).- 4.8 Comments on the Three Schools of Thought on MEM.- 5. Applications of the Maximum Entropy Method in Mathematics and Physics.- 5.1 Solution of Moment Problems.- 5.2 Solution of Integral Equations.- 5.3 Solution of Partial Differential Equations.- 5.4 Predictive Statistical Mechanics.- 5.5 Distributions of Particles Among Energy Levels.- 5.6 Classical Statistical Ensembles.- 5.7 Quantum Statistical Ensembles.- Appendices.- A. Cepstral Analysis.- A.1 Cepstral Analysis System.- A.2 I/O Relationship.-A.3 Properties of the Complex Cepstrum.- A.4 I/O Relationship for Minimum-Phase Input.- B. Image Restoration.- B.1 Image Formation.- B.2 Image Restoration.- B.3 Relationship Between Image Restoration and Spectral Estimation.- References.