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Compressed Sensing (CS) has been considered a very effective means of reducing energy consumption at the energy-constrained wireless body sensor networks for monitoring the multi-lead Electrocardiogram (MECG) signals. This paper develops the compressed sensing theory for sparse modeling and effective multi-channel ECG compression. A basis matrix with Gaussian kernels is proposed to obtain the sparse representation of each channel, which showed the closest similarity to the ECG signals. Thereafter, the greedy orthogonal matching pursuit (OMP) method is used to obtain the sparse representation of the signals. After obtaining the sparse representation of each ECG signal, the compressed sensing theory could be used to compress the signals as much as possible. Following the compression, the compressed signal is reconstructed utilizing the greedy orthogonal matching pursuit (OMP) optimization technique to demonstrate the accuracy and reliability of the algorithm. Moreover, as the wavelet basis matrix is another sparsifying basis to sparse representations of ECG signals, the compressed sensing is applied to the ECG signals using the wavelet basis matrix. The simulation results indicated that the proposed algorithm with Gaussian basis matrix reduces the reconstruction error and increases the compression ratio.