Real-time monitoring of vital physiological signals is of significant clinical relevance. Disruptions in the signals are frequently encountered and make it difficult for precise diagnosis. Thus, the ability to accurately predict/recover the lost signals could greatly impact medical research and application. We have developed new techniques of signal reconstructions based on iterative retraining and accumulated averaging of neural networks. The effectiveness and robustness of these techniques are demonstrated using data records from the Computing in Cardiology/PhysioNet Challenge 2010. The average correlation coefficient between prediction and target for 100 records of various target signals is about 0.9. We have also explored influences of a few important parameters on the accuracy of reconstructions. The developed techniques may be used to detect changes in patient state and to recognize intervals of signal corruption.