论文标题
来自部分边界测量的辐射源的数值重建
Numerical reconstruction of radiative sources from partial boundary measurements
论文作者
论文摘要
我们考虑通过在二维中的吸收和散射培养基中的固定辐射传输中的一个逆源问题。使用在边界的弧线上测量的角度分辨的辐射，我们提出了一种数值算法来恢复该弧的凸壳中的源。该方法涉及不稳定的步骤，即颠倒范围未关闭的有限运算符。我们表明，离散的逆的连续性常数最多可以通过离散步骤线性地增长，从而稳定了问题。
We consider an inverse source problem in the stationary radiative transport through an absorbing and scattering medium in two dimensions. Using the angularly resolved radiation measured on an arc of the boundary, we propose a numerical algorithm to recover the source in the convex hull of this arc. The method involves an unstable step of inverting a bounded operator whose range is not closed. We show that the continuity constant of the discretized inverse grows at most linearly with the discretization step, thus stabilizing the problem.
