Signal processing requires the efficient representation and processing of data. In an emerging trend the compressed signals gives the collection of linear projections of a sparse signal and information for reconstruction. In this paper, we propose that an application of compressed sensing in the field of signal processing, particularly electroencephalogram (EEG) collection and storage. The proposed framework is based on the EEG signals are sparse in a Gabor frame. Gabor frames are commonly used in science and engineering to synthesize signals from, or to decompose signals into, building blocks which are localized in time and frequency. The sparsity of EEG signals in a Gabor frame is utilized for compressing the signals. The matching pursuit algorithm is shown to be effective in the recovery of the original EEG signals from a small number of projections. The OMP algorithm improves the efficiency of finding the frequency-time atoms and rapid noise rectification. The experiments results are investigated up to 100 iterations and reduction of noise in weak signals.