Ill-Posedness and Accuracy in Connection with the Recovery of a Single Parameter from a Single Measurement

Abstract

A particular one-parameter problem, that of the reflection and refraction of a plane wave at a planar boundary between two media, which can be solved in closed form in both the direct and inverse contexts, is chosen to illustrate the ill-posed nature of a class of more general inverse problems and to show how the quality of the reconstruction of the parameter varies with the accuracy of the data on the one hand, and the accuracy of the interaction model employed in the inversion scheme on the other hand.

Keywords:

• Ill-posed
• One-parameter Problem