Neural-network approach for optical tomography

Abstract

The problem of optical tomography reconstruction is an ill-posed problem and the errors in the measurement data will be amplified in the reconstructed results. In order to fix the problem of ill-posedness, some a priori information should be incorporated in the process of reconstruction. In this paper, a Gibbs distribution with binary line process is introduced as the a prior image model, which can result in a global smoothness with sharp edges. Under this model the reconstruction can be realized in the Bayesian framework by maximizing the a posteriori probability. In order to solve the above mixed binary and continuous optimization problem, a coupled gradient neural network is proposed, in which the optimization can be realized following the evolution of the neural network by a proper definition of the energy function of it. To define the dynamics of the network, an algorithm based on the gradient tree is proposed for the gradient computation of the energy function with respect to optical parameters. Experimental results show that the proposed algorithm can be realized effectively with the proposed neural network and the quality of the reconstructed results can be significantly improved by the introduction of the prior mixed continuous and binary image model.