线性与非线性单调性基形状重建方法的比较
Comparison of linear and non-linear monotononicity-based shape reconstruction using exact matrix characterizations
AI总结：
本文比较了基于精确矩阵特征的线性和非线性单调性方法在电导率不均匀性检测中的应用，证明两种方法在单位盘域内重建结果基本相同。
摘要：
检测电导率不均匀性是电阻抗断层成像逆问题的特例，可导致快速直接重建方法。一种方法可在合理假设下，基于Neumann到Dirichlet映射（非线性）或其Fréchet导数（线性）的单调性性质，精确表征不均匀性。本文在存在测量噪声的情况下比较了非线性和线性方法，并通过数值实验证明两种方法在单位盘域内重建结果基本相同。为保证公平比较，使用精确矩阵特征来探测单调性关系，以避免来自PDE数值解和数值积分的误差。使用Neumann到Dirichlet映射的特殊分解，使非线性方法在单位盘几何中与线性方法具有相同的速度。
英文摘要：
Detecting inhomogeneities in the electrical conductivity is a special case of the inverse problem in electrical impedance tomography, that leads to fast direct reconstruction methods. One such method can, under reasonable assumptions, exactly characterize the inhomogeneities based on monotonicity properties of either the Neumann-to-Dirichlet map (non-linear) or its Fréchet derivative (linear). We give a comparison of the non-linear and linear approach in the presence of measurement noise, and show numerically that the two methods give essentially the same reconstruction in the unit disk domain. For a fair comparison, exact matrix characterizations are used when probing the monotonicity relations to avoid errors from numerical solution to PDEs and numerical integration. Using a special factorization of the Neumann-to-Dirichlet map also makes the non-linear method as fast as the linear method in the unit disk geometry.
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。
