In tele-monitoring, wireless body area networks (WBANs), sleep analysis and other applications involving electroencephalogram (EEG) signal, due to the high number of EEG recording channels, long recording time and several repetition of recordings to reach the highest signal-to-noise ratio, the amount of acquired data by the sensors is too large, demanding use of some compression procedure. Compressed sensing can be considered as one of the most effective compression methods in terms of compression ratio, which needs the underlying signal be sparse or have sparse representation in an appropriate domain. EEG signal is not sparse in time domain, therefore, in this paper correlation based weighted recursive least squares dictionary learning algorithm (CBW-RLS) is proposed that uses between-channel correlations to sparsify EEG signals. Due to the low-rank structure of EEG signals, exploiting between-channel correlations increase the sparsity level of the model while reducing the computational cost of dictionary learning procedure. This is done by merely updating the dictionary atoms which are involved in the sparse model of the previous data, reducing the total number of data used at each iteration and speeding up the dictionary learning algorithm. The simulation results show that the proposed method has better performance in terms of both quality of the EEG reconstruction and the computational cost compared to the other methods.