New Stability Estimates for the Inverse Acoustic Inhomogeneous Medium Problem and Applications

This paper is concerned with the scattering of time-harmonic acoustic waves by inhomogeneous media. We study the problem to recover the refractive index from far field measurements and from near field mesurements. We establish logarithmic stability estimates for these problems using a priori information with respect to Sobolev norms and a priori information about the support of the inhomogeneity. Our results improve previous estimates due to Stefanov by giving an explicit exponent in the logarithmic estimate, by using the L2 -norm for far field patterns, and by dropping the assumption that the refractive indices are close together. These improvements make it possible to prove convergence rates for iterative regularization methods.