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. © 2008 Elsevier Inc. All rights reserved.
Stefanov, P., & Uhlmann, G. (2009). Linearizing non-linear inverse problems and an application to inverse backscattering. Journal of Functional Analysis, 256(9), 2842–2866. https://doi.org/10.1016/j.jfa.2008.10.017