Inverse problem

Summary

An inverse problem asks for the causes of observed effects: to recover the parameters of a model from measured data that the model produces. The forward problem goes the other way and computes the data from known parameters. Inverse problems are often ill-posed in the sense of Hadamard: small errors in the data can cause large errors in the answer. So they need regularization. Examples are medical imaging, seismic exploration of the Earth, and the Calderón problem.