黑体辐射反问题的正则化Lanczos方法

Regularizing Lanczos Method for Inverse Blackbody Radiation Problem

黑体辐射反问题就是利用测量的黑体辐射能量谱确定黑体的区域温度分布。本文将该问题离散化为欠定线性不适定问题,提出求解欠定线性不适定问题的正则化L anczos方法。该方法基于L anczos双对角化过程,用一系列小型线性方程组逼近原不适定问题,应用截断SVD正则化方法使迭代稳定化,并用L-曲线确定相应的正则化参数。数值结果说明了新方法的有效性,并说明了在观测数据出现误差的情况下新方法也能有效地重构区域温度分布。

The inverse blackbody radiation problem is used for determining the area-temperature distribution of a blackbody from measured total radiated power spectrum. In this paper, the problem is discreted to an under-determined linear ill-posed system. A regularizing Lanczos method is presented for the solution of the linear ill-posed problem. The method is based on the Lanczos bidiagonalization process, which yields a sequence of small linear systems approximating the original ill-posed pro blem. The truncated SVD regularization is used to stabilize the iteration. The L-curve is used to determine the regularization parameter. Numerical results show the potential of the proposed method. Examples include a robust reconstruction in the presence of noise corrupted data.