散射测量中不均匀体重构的离散化与正则化
Discretization and regularization for the reconstruction of inhomogeneities by scattering measurements
AI总结：
本文提出通过离散化和正则化方法，利用有限次声波散射测量重构不均匀体的反问题解决方案。
摘要：
我们考虑在时谐设定下，通过有限次声波散射测量来重构不均匀体的反问题。我们将重构过程设定为一个完全离散的变分问题，并引入正则化。此类问题依赖于多种参数，即测量次数、正则化参数和离散化参数，即对亥姆霍兹型方程未知系数的网格大小。我们通过收敛性分析表明，可以通过精心选择这些参数，使得该离散正则化最小问题的解能够很好地近似反问题所寻求的解。
英文摘要：
We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem with regularization. Such a problem depends on a variety of parameters, that is, the number of measurements, the regularization parameter and the discretization parameter, namely the size of the mesh on which we discretize the unknown coefficients of the Helmholtz type equation modelling our physical system. We show, through a convergence analysis, that one can carefully choose these parameters in such a way that the solution to this discrete regularized minimum problem is a good approximation of the looked-for solution to the inverse problem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
