Optimizing Neural-Network Supported Acoustic Beamforming by Algorithmic Differentiation

In this paper we show how a neural network for spectral mask estimation for an acoustic beamformer can be optimized by algorithmic differentiation. Using the beamformer output SNR as the objective function to maximize, the gradient is propagated through the beamformer all the way to the neural network which provides the clean speech and noise masks from which the beamformer coefficients are estimated by eigenvalue decomposition. A key theoretical result is the derivative of an eigenvalue problem involving complex-valued eigenvectors. Experimental results on the CHiME-3 challenge database demonstrate the effectiveness of the approach. The tools developed in this paper are a key component for an end-to-end optimization of speech enhancement and speech recognition.