In this paper, a segment of the electroencephalogram (EEG) signal of a subject is viewed as outcomes of a single and a joint two random variables. The Shannon entropy (self information) contained in the single random variable and the mutual information associated with the joint two random variables can be used for the diagnosis of Alzheimer’s disease. It is shown that the self information may provide diagnostic error while the mutual information provides accurate and significant diagnosis. This can be justified by the following fact. The mutual information between a current sample and a delayed one of the EEG signal is a quantitative measure for the information of the current sample contained in the past one. Thus, this mutual information is related to the subject memory, which experiences a problem in Alzheimer’s disease.

In this paper, an adaptive approach using the least-mean-square lattice (LMSL) is proposed for the segmentation and tracking of the electro-encephalogram (EEG) signal. In the proposed approach, the time-trajectories of the reflection coefficients of the adaptive lattice predictor as well as the on-line power spectrum estimate are used as classification, segmentation and tracking parameters. The adaptive lattice predictor consists of cascaded similar first-order sections. Theses sections are independent due to the orthogonality principle linked to the least-mean square (LMS) algorithm. Therefore, on-line adding a new section makes no influence on the values of the coefficients of the preceding sections. Such property of the adaptive lattice predictor is not valid when the direct-form linear prediction filter is employed. Further advantage of the lattice predictor is the fast convergence due to independence of the successive sections, which yields no matrix computation. Results for tracking sleep spindles of computer-generated and real-world EEG data are presented to show the significant usefulness of the proposed approach. It is shown that an adaptive lattice predictors consisting of three up to four sections are satisfactory for the detection and tracking of the sleep spindles. A short-time (i.e., sliding window) implementation of Burg’s method (STBM) for computing the reflection coefficients of the lattice predictor is also suggested and examined. This method shows that the time-trajectories of the lattice coefficients, the on-line power spectrum and a proposed quantitative measure are capable of distinguishing between the EEG from normal healthy subject and the EEG from Alzheimer patient subject.

A quantitative electroencephalogram (qEEG) index for the evaluation and monitoring of cortical health in ischemic brain injury is presented. The proposed qEEG index, called the subbands spectral complexity distance (SSCD), measures the distance between a vector of subbands spectral complexities computed from the investigated EEG and a one computed from normal EEG. For the computation of the SSCD, the spontaneous power spectral density of the EEG signal is estimated using the time-varying autoregressive (TV-AR) model, decomposed into subbands and the spectral complexity of each subband is computed. Results of evaluating human EEG data are presented to show the usefulness of the proposed SSCD index. It is shown that the index increases during the time-segments of ischemic brain injury while decreases during the normal and recovery segments. This can be explained by the fact that the ischemic brain injury may increase the irregularity of the EEG signal and therefore the power spectral density becomes more complex with ischemic brain injury.