Multifrequency generalization of the Novikov algorithm for the two-dimensional inverse scattering problem

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).…”

Numerical approximation of the potential in the two-dimesional inverse scattering problem

“…Therefore, the inverse scattering problem can be stated as follows: Given the far field data u∞(θ , θ, k), for some values of θ ∈ S 1 , θ ∈ S 1 and k ∈ R, find a compactly supported V (x) ∈ L ∞ (R 2 ) that satisfies (5), where u is the solution of (4). Note that u∞ depends on three variables while V only depends on two.…”

Evaluation of inversion approaches for guided wave thickness mapping

“…which each comprise two core features: a set of physical assumptions which are used to describe how the waves propagate through the domain and a mathematical inversion method, which is used to calculate the best solution which fits the data. These three algorithms cover the majority of the acoustic wave speed inversion approaches used, and are the focus of this paper as they have been demonstrated to be fast, robust and practical for a wide range of configurations, but it is recognized that alternative approaches exist, such as full wave inversion [26] and the Novikov algorithm [27].…”