New Global Stability Estimates for Monochromatic Inverse Acoustic Scattering

Abstract

We give new global stability estimates for monochromatic inverse acoustic scattering. These estimates essentially improve estimates of [P. Hähner, T. Hohage, SIAM J. Math. Anal., 33(3), 2001, 670-685] and can be considered as a solution of an open problem formulated in the aforementioned work.

Error Estimates for Phaseless Inverse Scattering in the Born Approximation at High Energies

“…There are many important results on the former inverse scattering problem with phase information; see [3,4,6,7,8,9,12,13,14,15,16,17,18,22,23,24,25,28] and references therein. In particular, it is well known that the scattering amplitude f uniquely determines v via the Born approximation formulas at high energies:…”

Verification of a variational source condition for acoustic inverse medium scattering problems

“…This estimate was improved in [29] by choosing Y as an L 2 space and making the exponent µ explicit with µ ≤ 1. Recently, improved estimates were established in [31] where µ → ∞ as the smoothness exponent of the Sobolev ball K tends to ∞. Lower bounds in [30,40] show that such upper bounds are essentially optimal.…”

Explicit Formulas and Global Uniqueness for Phaseless Inverse Scattering in Multidimensions

“…Therefore, Problem 1.2 is of particular interest from the applied point of view in the framework of quantum mechanical inverse scattering. However, in the literature many more results are given on Problem 1.1 (see [2,3,[5][6][7][8][9][10][11][12][13][14][15][16][17][23][24][25][26][27][28][29][30][31][32][34][35][36][37] and references therein) than on Problem 1.2 (see chapter X of [7] and recent works [19,20] and references therein, where in [19,20] some similar problem is considered).…”