| 摘要 | 第4-5页 |
| Abstract | 第5-6页 |
| 目录 | 第7-10页 |
| Contents | 第10-13页 |
| Chapter 1 Introduction | 第13-30页 |
| 1.1 Some Background Information on Image processing | 第13-17页 |
| 1.2 Brief Background of PDE's In Image Processing | 第17-19页 |
| 1.3 Literature Review | 第19-26页 |
| 1.4 Objectives Of The Research | 第26-27页 |
| 1.5 Preliminaries | 第27-30页 |
| Chapter 2 Strictly Convex Modification of Total Variation Model For Image Denoising | 第30-44页 |
| 2.1 Introduction | 第30页 |
| 2.2 Proposed Model | 第30-34页 |
| 2.2.1 The Energy Functional | 第30-32页 |
| 2.2.2 The Associated Evolution Equation | 第32-34页 |
| 2.3 The Minimization Problem | 第34-35页 |
| 2.3.1 Existence and Uniqueness of Solution to the Minimization Problem | 第34-35页 |
| 2.4 Existence and Uniqueness for the Evolution Equation | 第35-44页 |
| 2.4.1 Definition of the Weak Solution | 第35-36页 |
| 2.4.2 Approximating Energy Functional | 第36-39页 |
| 2.4.3 Existence and Uniqueness of the Solution of the Evolution Problem | 第39-42页 |
| 2.4.4 Large Time Behavior | 第42-43页 |
| 2.4.5 Summary | 第43-44页 |
| Chapter 3 Alternative Variational Framework For Image Denoising | 第44-62页 |
| 3.1 Introduction | 第44页 |
| 3.2 Proposed Model | 第44-48页 |
| 3.2.1 The New Framework For Energy Functional | 第45-46页 |
| 3.2.2 Summary On The Characterization of Growth of the Coefficient Function | 第46-48页 |
| 3.3 The Minimization Problem | 第48-50页 |
| 3.3.1 Existence and Uniqueness of Solution to the Minimization Problem | 第48-49页 |
| 3.3.2 The Associated Evolution Equation | 第49-50页 |
| 3.4 Weak Solution to the Flow Associated with the Minimization Problem | 第50-62页 |
| 3.4.1 Existence of the Solution of the Approximate Evolution Problem | 第51-57页 |
| 3.4.2 Existence and Uniqueness of the Solution to the Evolution Problem | 第57-60页 |
| 3.4.3 Summary | 第60-62页 |
| Chapter 4 Multiplicative Noise Reduction Model Based on Logarithmic Reg-ularization | 第62-73页 |
| 4.1 Introduction | 第62-65页 |
| 4.2 Proposed Model for Multiplicative Noise Reduction | 第65-66页 |
| 4.3 Existence and Uniqueness for the Minimization Problem | 第66-68页 |
| 4.4 The Evolution Problem | 第68-73页 |
| 4.4.1 Semi-Discrete Version of Evolution Equation | 第68-69页 |
| 4.4.2 Existence and Uniqueness of the Solution Sequence for the Dis-crete Minimization Problem | 第69-70页 |
| 4.4.3 Euler Lagrange Equation for the Discrete Minimization Problem | 第70页 |
| 4.4.4 Convergence Of The Solution Sequence to the minimizer u | 第70-71页 |
| 4.4.5 Summary | 第71-73页 |
| Chapter 5 Numerical Experiments | 第73-93页 |
| 5.1 Introduction | 第73-74页 |
| 5.2 Numerical Schemes | 第74-83页 |
| 5.2.1 Experiment Ⅰ | 第75-77页 |
| 5.2.2 Experiment Ⅱ | 第77-83页 |
| 5.3 Discussion of the Results | 第83-89页 |
| 5.3.1 Results From Experiment Ⅰ | 第83-87页 |
| 5.3.2 Results From Experiment Ⅱ | 第87-89页 |
| 5.4 Experiment Ⅲ (Multiplicative Denoising) | 第89-93页 |
| 5.4.1 PM-Scheme | 第89-90页 |
| 5.4.2 AOS-Scheme | 第90-93页 |
| 结论 | 第93-95页 |
| Conclusion | 第95-98页 |
| References | 第98-107页 |
| List of Publications | 第107-109页 |
| Acknowledgement | 第109-111页 |
| Resume | 第111页 |
