论文标题
卡尔德隆（Calderón
Calderón's Inverse Problem with a Finite Number of Measurements II: Independent Data
论文作者
论文摘要
我们证明了Gel'Fand-Calderón在Schrödinger方程的逆问题的本地Lipschitz稳定性估计。主要的新颖性是只有有限数量的边界输入数据，并且这些数据属于未知电位，只要它属于$ l^\ infty $的已知有限维子空间。 Calderón问题的类似结果是作为推论而获得的。这对作者在几个方面的两个先前结果进行了改善，即测量的数量和相对于不施加错误的误差的稳定性。还提出了一种基于稳定性结果的新的迭代重建方案，为此，我们证明了迭代次数的指数收敛性和相对于数据中的噪声以及对错误的误差的稳定性。
We prove a local Lipschitz stability estimate for Gel'fand-Calderón's inverse problem for the Schrödinger equation. The main novelty is that only a finite number of boundary input data is available, and those are independent of the unknown potential, provided it belongs to a known finite-dimensional subspace of $L^\infty$. A similar result for Calderón's problem is obtained as a corollary. This improves upon two previous results of the authors on several aspects, namely the number of measurements and the stability with respect to mismodeling errors. A new iterative reconstruction scheme based on the stability result is also presented, for which we prove exponential convergence in the number of iterations and stability with respect to noise in the data and to mismodeling errors.
