Haar wavelet decomposition of EEG signal for ocular artifact de-noising: a mathematical analysis

The de-noising of ocular artifacts from the electroencephalogram (EEG) signals based on existing filtering techniques results in a substantial loss of data. In our recent research, we have proposed the use of Haar wavelets for selective detection of the ocular artifacts and a control subsystem for their subsequent removal. Further, the application of this procedure to Alzheimer's EEG lead to the development of an efficient system for the early detection of the disease in clinical EEG recording itself. A detailed analysis of the Haar wavelet basis function and the EEG signal during the moments when the eye blinks occur produces interesting explanations for the success of this novel technique. This paper analyzes the process from a mathematical perspective and proposes a theory based on the properties of the Dirac-delta function and its relation to the ocular artifacts in normal and Alzheimer's EEG. The pre-seizure spike discharges occurring due to epilepsy also provide valuable information that is appropriate for testing the analysis and hence, are also examined.