In this paper, a new monaural singing voice separation algorithm is presented. This field of signal processing provides important information in many areas dealing with voice recognition, data retrieval, and singer identification. The proposed approach includes a sparse and low-rank decomposition model using spectrogram of the singing voice signals. The vocal and non-vocal parts of a singing voice signal are investigated as sparse and low-rank components, respectively. An alternating optimization algorithm is applied to decompose the singing voice frames using the sparse representation technique over the vocal and non-vocal dictionaries. Also, a novel voice activity detector is presented based upon the energy of the sparse coefficients to learn atoms related to the non-vocal data in the training step. In the test phase, the learned non-vocal atoms of the music instrumental part are updated according to the non-vocal components captured from the test signal using domain adaptation technique. The proposed dictionary learning process includes two coherence measures: atom-data coherence and mutual coherence to provide a learning procedure with low reconstruction error along with a proper separation in the test step. The simulation results using different measures show that the proposed method leads to significantly better results in comparison with the earlier methods in this context and the traditional procedures.
