An innovative method of single-channel blind source separation is proposed. The proposed method is a complex-valued non-negative matrix factorization with probabilistically optimal L1-norm sparsity. This preserves the phase information of the source signals and enforces the inherent structures of the temporal codes to be optimally sparse, thus resulting in more meaningful parts factorization. An efficient algorithm with closed-form expression to compute the parameters of the model including the sparsity has been developed. Real-time acoustic mixtures recorded from a single-channel are used to verify the effectiveness of the proposed method.