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arXiv · 0809.0270

Linearizing non-linear inverse problems and an application to inverse backscattering

Plamen Stefanov·Gunther Uhlmann
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Abstract

We propose an abstract approach to prove local uniqueness and conditional Hölder stability to non-linear inverse problems by linearization. The main condition is that, in addition to the injectivity of the linearization $A$, we need a stability estimate for $A$ as well. That condition is satisfied in particular, if $A^*A$ is an elliptic pseudo-differential operator. We apply this scheme to show uniqueness and Hölder stability for the inverse backscattering problem for the acoustic equation near a constant sound speed.

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Plamen Stefanov, Gunther Uhlmann. 2008-09-01. Linearizing non-linear inverse problems and an application to inverse backscattering. https://arxiv.org/abs/0809.0270

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