论文标题
一些基于最小化的逆问题公式及其正则化的应用示例
Some application examples of minimization based formulations of inverse problems and their regularization
论文作者
论文摘要
In this paper we extend a recent idea of formulating and regularizing inverse problems as minimization problems, so without using a forward operator, thus avoiding explicit evaluation of a parameter-to-state map.我们这样做是通过以这种最小化形式重塑三个申请示例，即（a）使用完整的电极模型（b）鉴定磁通量测量值的非线性磁通透性（c）从微phone阵列阵列测量中定位声源的非线性磁通透性。为了建立针对这些问题的正规化方法的融合，我们首先扩展了现有理论。特别是，我们利用了这样一个事实，即观察值是有限的维度，以便可以使用观察操作员的倒置在某种程度上单独完成嘈杂数据的反转。这种新方法实际上适用于广泛的现实问题。
In this paper we extend a recent idea of formulating and regularizing inverse problems as minimization problems, so without using a forward operator, thus avoiding explicit evaluation of a parameter-to-state map. We do so by rephrasing three application examples in this minimization form, namely (a) electrical impedance tomography with the complete electrode model (b) identification of a nonlinear magnetic permeability from magnetic flux measurements (c) localization of sound sources from microphone array measurements. To establish convergence of the proposed regularization approach for these problems, we first of all extend the existing theory. In particular, we take advantage of the fact that observations are finite dimensional here, so that inversion of the noisy data can to some extent be done separately, using a right inverse of the observation operator. This new approach is actually applicable to a wide range of real world problems.
