In this paper the stability of inverse problems is discussed. It is taken into account that in inverse problems the structure of the solution space is often completely different from the structure of the data space, so that the definition of stability is not trivial. We solve this problem by assuming that under experimental conditions both the model and the data can be characterized by a finite number of parameters. In the formal definition that we present, we compare distances in data space and distances in model space under variations of these parameters. Moreover, a normalization is introduced to ensure that these distances do not depend on physical units. We note that it is impossible to obtain an objective estimate of stability due to the freedom one has in the choice of the norm in the solution space and the data space. This definition of stability is used to examine the stability of the Marchenko equation. It is shown explicitly that instabilities arise from the non-linearity of the inverse problem considered.
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- Stability Estimates for Inverse Problems
H. J. S. Dorren
R. K. Snieder
- Springer Netherlands
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