Artifacts are disturbances that may occur during signal acquisition and may affect their processing. The aim of this paper is to propose a technique for automatically detecting artifacts from the electroencephalographic (EEG) recordings. In particular, a technique based on both Independent Component Analysis (ICA) to extract artifactual signals and on Renyi's entropy to automatically detect them is presented. This technique is compared to the widely known approach based on ICA and the joint use of kurtosis and Shannon's entropy. The novel processing technique is shown to detect on average 92.6% of the artifactual signals against the average 68.7% of the previous technique on the studied available database. Moreover, Renyi's entropy is shown to be able to detect muscle and very low frequency activity as well as to discriminate them from other kinds of artifacts. In order to achieve an efficient rejection of the artifacts while minimizing the information loss, future efforts will be devoted to the improvement of blind artifact separation from EEG in order to ensure a very efficient isolation of the artifactual activity from any signals deriving from other brain tasks.