Recovery of Event Related Potential Signals using Compressive Sensing and Kronecker Technique

Brain-computer interfaces (BCIs) are devices that are developed to enable the brain to communicate with a machine directly. These devices usually make use of event-related potential (ERP) component of electroencephalography (EEG) signals. BCIs have several applications, but perhaps the most important one is to communicate with the advance neuromuscular patients. P300 Speller is a method that was developed by making use of BCIs and ERPs to make it possible to communicate with a computer through EEG recordings. The sensitive nature of these signals makes it essential to make sure they have a high recovery rate once they have been compressed. Compressive sensing (CS) is a compression method which takes advantage of the potential sparsity of the signals and aims to reconstruct a signal from a smaller number of measurements that is specified by the Nyquist theorem. CS has been studied in various signal processing areas. Because of the low power consumption and the elapsed time for generating CS measurements, CS became as one of the most efficient compression methods. In this work, we study the applicability of CS and its recovery quality for ERP signals. We run the experiments based on random and deterministic sensing matrices and two different sparsifying bases. The simulation results show that the ERP signal is very suitable for CS compression up to 75% compression ratio (CR). For the recovery phase, we investigate the effects of the recently developed preprocessing approach called Kronecker- based technique. By using Kronecker-based technique in recovery, we could recover the original signal with high accuracy up to 30 dB.