Problem of Reconstructing the Inhomogeneity Parameters of a Two-Dimensional Body from Acoustic Field Measurement Results

Abstract

Inverse problems requiring solutions arise in many areas of science and technology, such as medicine, manufacturing, etс. The main aim of the present paper is to formulate and solve an inverse problem, analyze solutions depending on the introduced noise and frequency of the source, and develop an algorithm of filtering solutions. We have obtained an integral equation of the first kind from measurement results at observation points. The wave number function of a body can be calculated using the formula and the result from solving the integral equation. A two-step method of reconstructing inhomogeneities of the body was applied. A solution of the problem depending on introduced errors was investigated. The algorithm for filtering noisy data was considered. Solving the problem using this method allows reconstruction of the internal structure of the body. The filtering method can help distinguish real inhomogeneities from noise.