Monday, August 5, 2019

Inverse Problems

Challenges when trying to solve inverse problems:

  • They may not have a unique solution.
  • Often, small changes in data cause arbitrarily large changes in solution.

Definition: (Hadamard, 1902)

If the solution of a problem is not unique, or it does not depend continuously on the data, then the problem is ill-posed.
  • Many inverse problems are also ill-posed.
  • For realistic problems (containing noise), we cannot hope to compute an exact solution.
Goal: Compute a meaningful approximation.
Approach: Use regularization.

https://faculty.alfaisal.edu/sites/default/files/styles/os_files_large/public/statar/files/inverse2.png?itok=yxIQvVh-