## Abstract

Convolutive blind source separation (CBSS) that exploits the sparsity of source signals in the frequency domain is addressed in this paper. We assume the sources follow complex Laplacian-like distribution for complex random variable, in which the real part and imaginary part of complex-valued source signals are not necessarily independent. Based on the maximum a posteriori (MAP) criterion, we propose a novel natural gradient method for complex sparse representation. Moreover, a new CBSS method is further developed based on complex sparse representation. The developed CBSS algorithm works in the frequency domain. Here, we assume that the source signals are sufficiently sparse in the frequency domain. If the sources are sufficiently sparse in the frequency domain and the filter length of mixing channels is relatively small and can be estimated, we can even achieve underdetermined CBSS. We illustrate the validity and performance of the proposed learning algorithm by several simulation examples.

Original language | English |
---|---|

Article number | 4244519 |

Pages (from-to) | 1551-1563 |

Number of pages | 13 |

Journal | IEEE Transactions on Audio, Speech and Language Processing |

Volume | 15 |

Issue number | 5 |

DOIs | |

Publication status | Published - Jul 2007 |

Externally published | Yes |

## Keywords

- Complex Laplacian-like distribution
- Convolutive blind source separation (CBSS)
- Frequency domain
- Permutation problem
- Probability density function
- Sparse representation (SR)