The Maximum Entropy Method [E-Book] / by Nailong Wu.
Wu, Nailong, (author)
Berlin, Heidelberg : Springer, 1997
XII, 327 p. online resource.
englisch
9783642606298
10.1007/978-3-642-60629-8
Springer Series in Information Sciences ; 32
Full Text
Table of Contents:
  • 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.