线性逆问题求解的多尺度降阶模型

Reduced Order Model for Solving Linear Inverse Problem

基于相对误差协方差矩阵信息,该文给出线性逆问题求解的多尺度降阶模型,把高阶模型的求 解问题转化为一个近似的低阶模型再进行求解.利用该降阶模型可以得到与完全模型相当的估计效果,同时 又能大大降低逆算法的计算量,从而有效地解决逆问题求解中计算复杂度过高的难题,增强逆问题求解算法 的可实施性.采用降阶模型进行求解还可以增加那些提供显著信息的点的估计精度.

Based on relative error covariance matrix (RECM) information, a reduced-order model is proposed for solving linear inverse problem. The reduced-order model turns the high order model into an approximate lower order model, which can efficiently alleviate the computational load of the inversion algorithm. Thus, the computational complexity difficulty arose in the solution of linear inverse problem can be conquered, and this in turn promotes the implementation of the inversion algorithm. In addition, the reduced-order model can improve the estimate precision of those points that provide significant information to the reconstruction of the object.