A Novel Source Enumeration Method Based on Sparse Representation

A novel source enumeration method based on criterion of searching for the best-matched preset sparse dictionary is presented in this paper, which is applicable under the condition of both white and colored noise. In this method, different source numbers are mapped with different sparse dictionaries innovatively in advance, which are constructed by utilizing the K-SVD algorithm and the training data under the same SNR. Then, in the source enumeration stage, all the preset dictionaries are employed to sparsely encode the observed signal through the orthogonal matching pursuit (OMP) algorithm, and the best-matched one which corresponds to the correct source number leads to the least information loss after sparse encoding. Due to the difficulty of directly evaluating the information loss through each error signal which is the difference between the observed signal and the sparse reconstructed signal, the energy norm for the singular values, which is calculated after performing singular value decomposition (SVD) on error signal, is proposed to reflect the information loss indirectly. Simultaneously, the source number corresponding to the best-matched preset sparse dictionary is the final estimated result. The experimental results show the superiority of our proposed method compared to other advanced methods.