Alexander D. Klose将联合差分方法用于光学层析图像重建的梯度计算中,但给出的对光学参量的求导算法有局限,他的算法只能实现对边界点光学参量的导数计算,而无法实现对内部点光学参量导数的计算,会导致图像重建失败。在联合差分算法的基础上,研究了针对内部点光学参量的求导方法,给出了一种基于树形结构的对内部点光学参量求导的策略。具体实现时,为了降低计算复杂度,采用近似梯度计算方法。算法的仿真实验结果表明:该方法可以有效地实现对内部点光学参量的导数计算,提出的近似计算方法可降低梯度计算复杂度,提高运算速度,并可得到良好的图像重建质量。

Adjoint differentiation method is used in reconstruction algorithm for optical tomography by Alexander D. Klose, but the algorithm of getting derivatives with respect to optical parameters is mistakenly proposed by him, and it can only implement the computation of derivative with respect to optical parameters on the boundary, those derivatives with respect to the internal parameters cannot be obtained there. This will lead to the failure of the reconstruction. Based on the adjoint differentiation method, an improved algorithm with a tree structure is proposed for the computation of derivatives, and a specific method about the derivative with respect to internal optical parameters is put forward. In order to decrease the computation complexity, an approximate strategy about gradient computation is adopted in the experiment. Experimental results show that this kind of algorithm can implement the computation of derivatives with respect to internal optical parameters effectively. The approximate algorithm can make the computation less complex, improve the speed of computation and get good quality of reconstruction at the same time.