论文标题
盒子约束和加权稀疏正规化，用于识别椭圆pdes中的来源
Box constraints and weighted sparsity regularization for identifying sources in elliptic PDEs
论文作者
论文摘要
我们探索使用边界数据识别椭圆PDE中源的可能性。即使相关的前向操作员有较大的空空间，但事实证明，结合加权稀疏正则化的盒子约束可以实现恒定/强度恒定/强度的准确恢复源。此外，对于具有不同强度的来源，反向解决方案的支持将是真实来源支持的子集。我们既展示了问题的分析，也介绍了一系列数值实验。我们的工作仅解决离散问题。 引入加权程序的原因是，标准（未加权）稀疏正规化无法为本文考虑的源识别任务提供足够的结果。该研究还由应用，例如，从重力场和反向散射的测量中恢复质量分布。我们根据欧几里得空间发展了方法和分析，因此我们的结果可以应用于许多问题。例如，结果同样适用于涉及筛选的泊松方程的模型，与使用Helmholtz方程的模型（具有较大和小波数）。
We explore the possibility for using boundary data to identify sources in elliptic PDEs. Even though the associated forward operator has a large null space, it turns out that box constraints, combined with weighted sparsity regularization, can enable rather accurate recovery of sources with constant magnitude/strength. In addition, for sources with varying strength, the support of the inverse solution will be a subset of the support of the true source. We present both an analysis of the problem and a series of numerical experiments. Our work only addresses discretized problems. The reason for introducing the weighting procedure is that standard (unweighted) sparsity regularization fails to provide adequate results for the source identification task considered in this paper. This investigation is also motivated by applications, e.g., recovering mass distributions from measurements of gravitational fields and inverse scattering. We develop the methodology and the analysis in terms of Euclidean spaces, and our results can therefore be applied to many problems. For example, the results are equally applicable to models involving the screened Poisson equation as to models using the Helmholtz equation, with both large and small wave numbers.
