基于稳健联合分块对角化的卷积盲分离

Robust Joint Block Diagonalization Based Convolutive Blind Source Separation

针对卷积盲分离问题,提出一种新的矩阵联合分块对角化(Joint block diagonalization,JBD)算法.现有的迭代非正交联合分块对角化算法都存在不收敛的情况,本文利用分离矩阵的特殊结构确保其可逆性,使得算法的迭代过程稳定.在已知矩阵分块结构的条件下,首先,将卷积盲分离模型写成瞬时形式,并说明其满足联合分块对角化结构;然后,提出联合分块对角化的代价函数,依据代价函数的最小化等价于矩阵中每个分块的范数最小化,将整个分离矩阵的迭代更新转化成每个分块的迭代更新;最后,利用最小化条件得到迭代算法.实数和复数两种情况下的算法都进行了推导.基本实验验证了新算法在不同条件下的性能;仿真实验中对在时域和频域都重叠的信号的卷积混合进行盲分离,实验结果验证了新算法具有更好的分离性能和更稳定的分离能力.

A new joint block diagonalization （JBD） algorithm is proposed to solve the convolutive blind source separation problem. The existing iterative algorithms may not converge to the correct solution. We use a special structured separation matrix which is always invertible to avoid the divergence of the algorithm. First, the convolutive mixture is rewritten as an instantaneous one which satisfies the joint block diagonalization model. Second, the cost function is built with the priori information of block structure. Then the whole matrix iteration is transformed into update of the every block sub-matrix in the sense that the minimization of the cost function is equivalent to the minimization of Frobenius norm of each block. The iterative algorithm is deduced both in the situations of real and complex models. Sanity check experiment has verified the good performance of the new algorithm in different conditions. In the application of blind separation of signals which are both overlaping in the time and frequency domains, simulation results demonstrate the better performance and more robust ability of the proposed Mgorithm, as compared to others.