Two-Parameter Regularization Algorithm for the Inverse Black Body Radiation Problem

The black body radiation inverse problem is to determine the black body's temperature distribution from its total radiated power spectrum, which is an ill-posed problem. A numerical algorithm for the inverse black body radiation problem is presented in this paper. Based on the Tikhonov regularization method, we introduce entropy as the second stable function to obtain a two-parameter regularization algorithm for the inverse black body radiation problem. Using the Gauss-Laguerre quadrature formula to discretize the integral term of the inverse black body radiation equation, the equation is converted into an ill-posed and lower-dimension system of two-parameter nonlinear algebraic equations. The regularization parameters are determined by the leave-one-out cross-validation method and selected by a two-dimension heat map. Numerical experiments show that our algorithm can get good inversion results only using 15 nodes, which means that less experimental measurement is needed. In particular, it should be pointed out that our algorithm can still maintain good calculation accuracy when the internal temperature distribution of the black body is unsmooth and there are breakpoints, while in this case, the calculation accuracy of the previous black body inversion algorithms is low.