Convolutive blind signal separation in acoustics by joint approximate diagonalization of spatiotemporal correlation matrices

We present an efficient algorithm for the blind signal separation (BSS) problem with convolutive signal mixtures, as it usually appears in acoustics, e.g., in the cocktail party problem. Since acoustical signals are typically nonstationary and nonwhite, we make use of these two statistical properties in the formulation of the blind cost function. In order to achieve true signal separation, the algorithm aims at finding a single polynomial matrix, the convolutive separation matrix that jointly diagonalizes a set of measured spatiotemporal correlation matrices. Minimizing the cost function turns out to be mathematically equivalent to a convolutive joint approximate diagonalization problem (CJAD). In order to increase the initial convergence rate, an Armijo line search is incorporated into the update. The final algorithm operates primarily in the frequency domain (fast convolution techniques) even though the cost function and gradient are formulated in the time domain. This approach reduces the computational complexity and avoids the so-called permutation problem.