《影像数学方法手册》对成像科学中使用的数学技术进行了全面的论述。材料分为两个中心主题,即逆问题(算法重建)和信号和图像处理。主题中的每个部分包括应用程序(建模)、数学、数值方法(使用案例示例)和开放问题。由该领域的专家撰写的报告在数学上是严谨的。
这个扩展和修订的第二版包含了对现有章节的更新和16个重要的数学方法,如图形切割,形态学,离散几何,偏微分方程,保形方法,等等。这些条目是交叉引用的,以便通过连接的主题轻松导航。该手册有印刷和电子两种形式,增加了200多幅插图和扩展的参考书目。
它将使应用数学的学生、科学家和研究人员受益。从事成像工作的工程师和计算机科学家也会发现这本手册很有用。
目录:
- Linear Inverse Problems
- Large-Scale Inverse Problems in Imaging
- Regularization Methods for Ill-Posed Problems
- Distance Measures and Applications to Multi-Modal Variational Imaging
- Energy Minimization Methods
- Compressive Sensing
- Duality and Convex Programming
- EM Algorithms
- Iterative Solution Methods
- Level Set Methods for Structural Inversion and Image Reconstruction
- Expansion Methods
- Sampling Methods
- Inverse Scattering
- Electrical Impedance Tomography
- Synthetic Aperture Radar Imaging
- Tomography
- Optical Imaging
- Photoacoustic and Thermoacoustic Tomography: Image Formation Principles
- Mathematics of Photoacoustic and Thermoacoustic Tomography
- Wave Phenomena
- Statistical Methods in Imaging
- Supervised Learning by Support Vector Machines
- Total Variation in Imaging
- Numerical Methods and Applications in Total Variation Image Restoration
- Mumford and Shah Model and its Applications to Image Segmentation andImage - - Restoration
- Local Smoothing Neighborhood Filters
- Neighborhood Filters and the Recovery of 3D Information
- Splines and Multiresolution Analysis
- Gabor Analysis for Imaging
- Shape Spaces
- Variational Methods in Shape Analysis
- Manifold Intrinsic Similarity
- Image Segmentation with Shape Priors: Explicit Versus Implicit - Representations
- Starlet Transform in Astronomical Data Processing
- Differential Methods for Multi-Dimensional Visual Data Analysis