2007 Volume 2 Pages S1015
We describe a neural network collocation method (NNCM) for tomographic image reconstruction with small amount of projection data, which has been successfully applied to the three-dimensional ionospheric tomography based on the dataset of signal delays from the GPS satellites. In NNCM the neural network is trained by minimizing an object function composed of squared residuals of the governing equations evaluated at the collocation points and some constraining conditions imposed usually by observation data. This method is applied not only to the computerized tomography but also to the analyses of various inverse problems such as the data assimilation, the parameter estimation, the time series prediction, and so on.
