作者：冯俊
页数：84
出版社：四川大学出版社
出版日期：2020
ISBN：9787569038484
电子书格式：pdf/epub/txt
内容简介
本书为学术专著。近年来，变分偏微分方程为基础的图像处理模型在众多任务场景（如图像去噪、图像重建、图像分割等）得到了广泛的应用。本书主要讨论了变分偏微分模型及其在图像处理中的应用，通过引入几种能量泛函构建了一个变分模型，用于处理多尺度噪声和多尺度边界；基于各向扩散模型提出了一个自适应动态耦合能量模型，并将模型应用于有限投影计算机断层成像之中；在各向异性扩散模型的基础上，针对地震资料去噪问题，提出了一个耦合能量变分模型；基于各向异性扩散和变分模态分解，提出了一个自适应混合扩散模型（AHD）并用于随机噪声去除。
作者简介
冯俊，成都理工大学副教授，主要研究方向为应用数学，油气地球物理新方法、新技术，计算机视觉，图像处理算法设计与分析等。先后在国内外学术期刊上发表论文10余篇，主持和参加了多个项目。周彬，西南石油大学副教授，主要研究方向为偏微分方程图像处理、数据挖掘、统计学习等。主持并完成国家自然科学基金等纵横向项目多项，在国内外期刊发表论文10余篇。
目录
Chapter 1 Continuous Level Anisotropic Diffusion
1.1 Introduction
1.2 Anisotropic diffusion and total variation
1.3 Continuous level anisotropic diffusion
1.3.1 Local adaptive anisotropic diffusion
1.3.2 Optimization of the threshold function
1.3.3 A nonlinear evolution system for noise removal
1.4 Numerical examples
1.5 Conclusions
Chapter 2 Anisotropic Diffusion for Image Reconstruction
2.1 Introduction
2.2 Total variation minimization
2.3 Adaptive dynamic combined energy reconstruction model
2.3.1 Dynamic combined energy model
2.3.2 Conjugate gradient method for model solving
2.4 Numerical experiments
2.4.1 Limited-view reconstruction
2.4.2 Limited-view reconstruction from limited angel
2.5 Conclusion
Chapter 3 Anisotropic Diffusion-Based Dynamic Combined Energy Model
3.1 Introduction
3.2 Anisotropic diffusion
3.3 Dynamic Combined Energy model
3.4 Examples
3.4.1 Synthetic data examples
3.4.2 Field data examples
3.5 Lonclusion
Chapter 4 Anisotropic Diffusion Model Using Variational Mode Dr
4.1 Introduction
4.2 Methods
4.2.1 Variational Mode Decomposition
4.2.2 Dynamic Combined Energy model
4.2.3 Adaptive Hybrid Diffusion model
4.3 Synthetic and field data application
4.3.1 Synthetic data example
4.3.2 Field data examples
4.4 Conclusion
Chapter 5 Anisotropic Diffusion Based Low Rank Tensor Decomposition ModeI
5.1 Introduction
5.2 The proposed method
5.2.1 Model overview
5.2.2 Patch grouping
5.2.3 CP decomposition
5.2.4 Patch aggregation
5.2.5 Model solution
5.2.6 The procedure of the TDTV method
5.3 Experimental results and discussion
5.3.1 Synthetic seismic data
5.3.2 Field seismic data
5.4 Conclusion
RefeFences
1.1 Introduction
1.2 Anisotropic diffusion and total variation
1.3 Continuous level anisotropic diffusion
1.3.1 Local adaptive anisotropic diffusion
1.3.2 Optimization of the threshold function
1.3.3 A nonlinear evolution system for noise removal
1.4 Numerical examples
1.5 Conclusions
Chapter 2 Anisotropic Diffusion for Image Reconstruction
2.1 Introduction
2.2 Total variation minimization
2.3 Adaptive dynamic combined energy reconstruction model
2.3.1 Dynamic combined energy model
2.3.2 Conjugate gradient method for model solving
2.4 Numerical experiments
2.4.1 Limited-view reconstruction
2.4.2 Limited-view reconstruction from limited angel
2.5 Conclusion
Chapter 3 Anisotropic Diffusion-Based Dynamic Combined Energy Model
3.1 Introduction
3.2 Anisotropic diffusion
3.3 Dynamic Combined Energy model
3.4 Examples
3.4.1 Synthetic data examples
3.4.2 Field data examples
3.5 Lonclusion
Chapter 4 Anisotropic Diffusion Model Using Variational Mode Dr
4.1 Introduction
4.2 Methods
4.2.1 Variational Mode Decomposition
4.2.2 Dynamic Combined Energy model
4.2.3 Adaptive Hybrid Diffusion model
4.3 Synthetic and field data application
4.3.1 Synthetic data example
4.3.2 Field data examples
4.4 Conclusion
Chapter 5 Anisotropic Diffusion Based Low Rank Tensor Decomposition ModeI
5.1 Introduction
5.2 The proposed method
5.2.1 Model overview
5.2.2 Patch grouping
5.2.3 CP decomposition
5.2.4 Patch aggregation
5.2.5 Model solution
5.2.6 The procedure of the TDTV method
5.3 Experimental results and discussion
5.3.1 Synthetic seismic data
5.3.2 Field seismic data
5.4 Conclusion
RefeFences
