Physiological signals, specially those related to cardiovascular function, are usually corrupted due to the number of degradation sources appearing in the acquisition process (noise, movements, etc.). If the power of these artifacts is close to the power of the signal, they cannot be removed and the affected epoch must be set aside. In this paper, we propose a novel methodology for reconstructing corrupted pieces based on signal modelling. The method consists of two stages: 1) estimation of the model parameters from the largest uncorrupted signal and 2) simulation of the model to achieve a new piece able to replace the corrupted one. Results on real data show that reconstructed pieces are valid in terms of statistical similarity, yielding anomaly-free realizations of the stochastic process modelling the acquired signal.