Frame-by-Frame Closed-Form Update for Mask-Based Adaptive MVDR Beamforming

Beamforming approaches using time-frequency masks have recently been investigated and have shown promising results for noise robust automatic speech recognition (ASR) in many tasks. The time-frequency masks are estimated to compute the spatial statistics of target speech and noise signals, and then the statistics are used to derive a beamformer. Although its effectiveness has been clearly shown in batch and blockwise processing, it has not been well extended to frame-by-frame processing, which is a very important procedure for many actual applications. In this paper, we derive a frame-by-frame update rule for a mask-based minimum variance distortion-less response (MVDR) beamformer, which enables us to obtain enhanced signals without a long delay by combining it with uni-directional recurrent neural network-based mask estimation. Based on the Woodbury matrix identity, our algorithm achieves a closed-form solution of the mask-based MVDR beamformer at every time frame without any matrix inversion. Experimental results show that our frame-by-frame beamformer outperforms baseline block-wise beamforming on the CHiME-3 simulation dataset even with a shorter time delay.