Abstract: To address the training problem of discrete process neural networks，two training algorithms based on numerical integration were proposed. The cubic spline integration and the parabolic interpolation integration were used in the hidden layer to deal with the time-domain aggregation of discrete samples and weights. The classical neurons were used in output layer. In order to improve the convergence ability of the network, the Levenberg-Marquard algorithm was employed to adjust the networks’ parameters. The effeciveness of the proposed algorithms was testified by applying the network to the restoration of a fuzzy image. Experimental results show that the performance of the two algorithms is relatively close and is superior to the Walsh transformation-based discrete process neural networks and spline function-based discrete process neural networks in both approximation ability and effect of image restoration, which reveals that the proposed methods of numerical integration have some potential in the performance improvement and application extension of discrete process neural networks.