Optical tomography reconstruction based on gradient tree

The adjoint differentiation scheme was first proposed by Alexander D. Klose for the reconstruction of optical tomography [J Q S R T 2002;72:715-32]. However, the scheme proposed there can only be employed for the computation of derivatives with respect to the optical parameters on the boundary, i.e. those derivatives with respect to the internal parameters cannot be obtained there, and as a result, the correct reconstructed result cannot be obtained with the gradient based optimization algorithms. In our paper, based on the adjoint differentiation scheme, a novel algorithm based on gradient tree is proposed for the computation of the derivatives with respect to both boundary and internal optical parameters. A scheme for approximate gradient calculation is also proposed for speeding up algorithm implementation. Experimental results show that the algorithm proposed performs well and good reconstruction results can be achieved.