Inverse Problems

Skills

This course aims to provide the student with skills to

• Formulate a complex data analysis problem as an inverse problem
• Describe and quantify data uncertainties and modeling errors
• Describe available prior (external) information using probabilistic models and methods
• Find probabilistic solutions to
  - Linear and weakly non-linear, Gaussian inverse problems
  - General (non-linear, non-Gaussian) inverse problems
• Analyze and validate solutions to inverse problems

Knowledge

This course will give the students a mathematical description of inverse problems as they

appear in connection with measurements and experiments in physical sciences. It teaches them to solve inverse problems with analytical and numerical methods. The students will study illposedness, numerical instability, non-uniqueness of solutions, and how noise propagates into uncertainty of the solutions.

Competences

Through the course the students will be able to identify inverse problems in various fields of physical sciences, classify them, and choose appropriate solution methods. The students will be able to find appropriate parameterizations, treat data uncertainties, and to evaluate the accuracy and resolution of the inverse solution.