论文标题
逆向声散射的迭代和功能分析算法的数值比较
Numerical comparison of iterative and functional-analytical algorithms for inverse acoustic scattering
论文作者
论文摘要
在这项工作中，考虑了基于迭代和功能分析算法的声学断层扫描问题的数值解决方案。这些算法的数学特性先前在R.G. Novikov的作品中描述了Schrödinger方程。在目前的工作中，对于二维标量Helmholtz方程式，迭代算法在重建中强度散射器的重建方面的效率以及功能分析方法在恢复强散射器中的优势。在波向量的空间中考虑了一个过滤过程，该过程还增加了迭代算法的收敛性。声速扰动的重建结果表明，在重建中强度散射器时，所考虑的算法的噪声免疫和分辨率可比。这项工作首次实施了反散射问题中迭代和功能分析算法的比较数值研究。
In this work the numerical solution of acoustic tomography problem based on the iterative and functional-analytical algorithms is considered. The mathematical properties of these algorithms were previously described in works of R.G.Novikov for the case of the Schrödinger equation. In the present work, for the case of two-dimensional scalar Helmholtz equation, the efficiency of the iterative algorithm in reconstruction of middle strength scatterers and advantages of the functional-analytical approach in recovering strong scatterers are demonstrated. A filtering procedure is considered in the space of wave vectors, which additionally increases the convergence of the iterative algorithm. Reconstruction results of sound speed perturbations demonstrate the comparable noise immunity and resolution of the considered algorithms when reconstructing middle strength scatterers. A comparative numerical investigation of the iterative and functional-analytical algorithms in inverse acoustic scattering problems is implemented in this work for the first time.
