Inversion of simulated positron annihilation lifetime spectrum using a neural network

Inversion of positron annihilation lifetime spectroscopy, based on a neural network Hopfield model, is presented in this paper. From a previous reported density function for lysozyme in water a simulated spectrum, without the superposition of statistical fluctuation and spectrometer resolution effects, was generated. These results were taken as the exact results from which the neural network was trained. The precision of the inverted density function was analyzed taking into account the number of neurons and the learning time of the neural network. A fair agreement was obtained when comparing the neural network results with the exact results. For example, the maximum of the density function, with a precision of 0.4% for the percentual relative error, was obtained for 64 neurons.