数字图像处理(Digital Image Processing)是通过计算机对图像进行去除噪声、增强、复原、分割、提取特征等处理的方法和技术。数字图像处理的产生和迅速发展主要受三个因素的影响:一是计算机的发展;二是数学的发展(特别是离散数学理论的创立和完善);三是广泛的农牧业、林业、环境、军事、工业和医学等方面的应用需求的增长。

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《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
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