Multichannel equalization in the KLT and frequency domains with application to speech dereverberation

Equalization of acoustic channels usually involves inversion of acoustic impulse responses (AIRs), and generally employs multichannel techniques. In this paper, we propose three equalization algorithms, one in the Karhunen-Loève transform (KLT) domain and the other two in the frequency domain. Our proposed algorithm in the KLT domain provides a platform to achieve equalization in conjunction with denoising. Existing multiple-input/output inverse theorem (MINT)-based non-adaptive algorithms require the inversion of a matrix with dimension that is proportional to the AIR length, and is computationally expensive. To overcome this limitation, we propose the frequency-domain algorithm which is computationally very efficient and thus can be employed for the equalization of high-order AIRs in practical applications. In addition, the frequency-domain method is more robust to AIR estimation errors. To achieve further reduction in the complexity without significant performance degradation, we then propose a modified version of the frequency-domain algorithm.