This paper proposes a new single-channel speech separation method based on sparse decomposition.The new method is based on the construction algorithms of quasi-KLT bases proposed in this paper.First,it is proved that based on the ideal quasi-KLT bases generated from the sources,both sources can be perfectly separated from a single mixture by l exp(0) optimization.Then,considering the fact that the ideal quasi-KLT bases cannot be obtained in practice,orthogonal matching pursuit (OMP) template-matching quasi-KLT bases generated from the single mixture are first proposed,and then perform single-channel speech separation by l exp(0) optimization using the OMP template-matching quasi-KLT bases.Finally,simulation results demonstrating the perfect separation of both sources from a single-channel speech mixture by l exp(0) optimization using ideal quasi-KLT bases,as well as the effective performance of single-channel separation of two speech sources using the OMP template-matching quasi-KLT bases are presented.