Mathematical Background

This section explains the mathematical concepts on which ODL is built.

• Linear Spaces
  • Definition and basic properties
  • Metric spaces
  • Normed spaces
  • Inner product spaces
  • Cartesian spaces
  • Weighted Cartesian spaces
  • Useful Wikipedia articles
• Discretizations
  • Mathematical background
  • Example
  • Useful Wikipedia articles
• Resizing Operators
  • Introduction
  • Basic setting
  • Restriction operator
  • Extension operators
  • Generalization to arbitrary dimension
• On the different notions of derivative
  • Derivative
  • Gradient
  • Hessian
  • Spatial Gradient
  • Subgradient
  • Notes on complex spaces
• Transformations
  • Fourier Transform
• Solvers
  • Primal-Dual Hybrid Gradient Algorithm (PDHG)
  • Proximal Operators