# Numerical results of solving 3D inverse scattering problem with non-over-determined data

## TL;DR

This paper presents a numerical method for solving the 3D inverse scattering problem with non-over-determined data, demonstrating its effectiveness through computational results, and builds on existing uniqueness theorems.

## Contribution

The paper introduces a novel numerical approach for the 3D inverse scattering problem with limited data, extending previous theoretical results to practical computation.

## Key findings

- Numerical method successfully reconstructs scattering objects from limited data.
- Computational results validate the effectiveness of the proposed approach.
- The method handles data with partial angular coverage and fixed incident direction.

## Abstract

We consider the 3D inverse scattering problem with non-over-determined scattering data. The data are the scattering amplitude $A(\beta, \alpha_0, k)$ for all $\beta \in S_\beta^2$, where $S_\beta^2$ is an open subset of the unit sphere $S^2$ in $\mathbb{R}^3$, $\alpha_0 \in S^2$ is fixed, and for all $k \in (a,b), 0 \leq a < b$. The basic uniqueness theorem for this problem belongs to Ramm \cite{R603}. In this paper, a numerical method is given for solving this problem and the numerical results are presented.