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

We propose an abstract approach to prove local uniqueness and conditional Hölder stability to nonlinear 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