In this paper a generalized minimum norm principle and/or a maximum entropy principle are used as general criteria, e.g. for reconstructing images or signals from noisy and incomplete projection data. The linear inverse problem is reformulated as an optimization problem and solved by a unified analog neural network. Moreover, in order to reduce the network complexity a new approach is proposed which makes it possible to construct simply and effectively a neural network containing only one single artificial neuron with an on chip adaptive learning algorithm. The correctness and performance of the proposed neural network architectures are illustrated by extensive computer simulation experiments.