Permutation entropy (PE) is a well-known and fast method extensively used in many physiological signal processing applications to measure the irregularity of time series. Multiscale PE (MPE) is based on assessing the PE for a number of coarse-grained sequences representing temporal scales. However, the stability of the conventional MPE may be compromised for short time series. Here, we propose an improved MPE (IMPE) to reduce the variability of entropy measures over long temporal scales, leading to more reliable and stable results. We gain insight into the dependency of MPE and IMPE on several straightforward signal processing concepts which appear in biomedical activity via a set of synthetic signals. We also apply these techniques to real biomedical signals via publicly available electroencephalogram (EEG) recordings acquired with eyes open and closed and to ictal and non-ictal intracranial EEGs. We conclude that IMPE improves the reliability of the entropy estimations in comparison with the traditional MPE and that it is a promising technique to characterize physiological changes affecting several temporal scales. We provide the source codes of IMPE and the synthetic data in the public domain. 
Improved multiscale permutation entropy for biomedical signal analysis: Interpretation and application to electroencephalogram recordings