ИСТИНА

The inverse scattering problem is considered. It means the reconstruction of internal structure of an object under study in the form of spatial distributions of its characteristics. Such characteristics are sound speed and absorption coefficient at each point of the object under study, in the case of the acoustic inverse scattering problem. The improved numerical implementation of the two-dimensional functional analytical algorithm [1–4] based on the use of the apparatus of angular harmonics is proposed. This apparatus allows, firstly, to increase the accuracy of the numerical implementation during the transition from continuous to sampled quantities. Secondly, it makes it convenient to analyze and fundamentally control the sufficiency (or insufficiency) of the available volume of initial sampled data and sampled values of subsequent functions calculated in the process of solving the inverse scattering problem. The numerical solution of the inverse problem has been performed for a number of model two-dimensional scatterers of large wave sizes (about 80–120 wavelengths) with a complicated internal structure. The high accuracy of the reconstruction of the quantitative values of the desired acoustic characteristics has been shown. One of the specific possible applications of the results is the urgent problem of reconstructing the breast pathologies [5]. The high resolution of the algorithm allows, in principle, to detect pathology at an early stage of its occurrence. The research was funded by the Russian Science Foundation (project No. 24-22-00192), https://rscf.ru/project/24-22-00192. REFERENCES 1. Grinevich P. G., Manakov S. V. Inverse scattering problem for the two-dimensional Schrödinger operator, the d-bar-method and nonlinear equations // Functional Analysis and its Applications. 1986. V. 20. N 2. P. 94–103. 2. Novikov R. G. The inverse scattering problem on a fixed energy level for the two-dimensional Schrödinger operator // Journal of Functional Analysis. 1992. V. 103. N 2. P. 409–463. 3. Novikov R. G. Rapidly converging approximation in inverse quantum scattering in dimension 2 // Physics Letters A. 1998. V. 238. N 2–3. P. 73–78. 4. Burov V. A., Rumyantseva O. D. Inverse wave problems of acoustic tomography. Pt. 4: Functional-analytical methods for solving the multidimensional acoustic inverse scattering problem. M.: URSS, 2024. 504 p. [in Russian]. 5. Li F., Villa U., Duric N., Anastasio M.A. 3D full-waveform inversion in ultrasound computed tomography employing a ring-array // Proceedings of SPIE. Medical Imaging 2023: Ultrasonic Imaging and Tomography. Eds. Boehm C., Bottenus N. 2023. V 12470. P. 124700K-1 – 124700K-6