Chapter 1 Introduction

1.1 Motivation

1.2 Outline of Book

1.3 Original Contributions

Chapter 2 Wavelet and Hidden Markov Model(HMM)

2.1 Wavelet Analysis

2.1.1 Integral Wavelet Transform

2.1.2 Discrete Wavelet Transform

2.1.3 Multiresolution Analysis(MRA)of L2(R)

2.1.4 Wavelet Packet

2.1.5 Two Dimensional Wavelets

2.2 Hidden Markov Model

2.2.1 From Markov Process to Markov Model

2.2.2 Elements of an Hidden Markov Model

2.2.3 The Three Basic Problems for HMM

2.2.4 Solution to Problem 1：Probability Evaluation

2.2.5 Solution to Problem 2："Optimal"State Sequence

2.2.6 Solution to Problem 3：Parameter Estimation

2.2.7 Continuous Observation Densities in HMMs

Chapter 3 Image Denoising on Wavelet Domain

3.1 Introduction

3.2 Important Statistical Preparations

3.2.1 Prior and Posterior Distribution

3.2.2 Markov Random Field

3.2.3 Maximum Likelihood Estimate

3.2.4 Expectation-Maximization(EM)

3.3 Description of Image Denoising

3.3.1 Gaussian White Noise

3.3.2 Signal and Noise Ratios

3.3.3 Criteria

3.4 Wavelet Thresholding

3.4.1 Hard and Soft Thresholding

3.4.2 Improvements of Wavelet Thresholding

3.5 Least Square Estimation

3.6 Spatial Image Denoising

3.6.1 New Frameworks

3.6.2 Denoising Results

3.7 Summary

Chapter 4 Spatial Wavelet Domain Hidden Markov Model

4.1 Preparations

4.1.1 Statistical Models and Wavelet

4.1.2 Gaussian Mixture Model

4.1.3 EM Algorithm

4.1.4 Least Square Estimation on Wavelet Domain

4.2 Wavelet Domain-Hidden Markov Models

4.2.1 Independent Mixture(IM)Model

4.2.2 Hidden Markov Tree(HMT)Model

4.2.3 Contextual Hidden Markov Model(CHMM)

4.3 Spatial Wavelet Domain-Hidden Markov Models

4.3.1 Gaussian Markov Field

4.3.2 Block

4.3.3 Template

4.3.4 EM Algorithm of the Block HMM

4.3.5 EM Algorithm of the Template HMM

4.3.6 Some Views about Improved WD-HMM

Chapter 5 Signal Denoising Using the Block HMM

5.1 Signal Denoising

5.2 The Signal Denoising Algorithm Using the Block HMM

5.3 Experimental Results and Discussion

5.4 Conclusions

Chapter 6 Image Denoising Using the Template HMM

6.1 Image Denoising

6.2 The Image Denoising Algorithm Using the Template HMM

6.3 Experimental Results and Discussion

6.4 Conclusions

Chapter 7 Conclusions and Perspectives

Bibliography