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This article proposes methods that can optimize a Convolutional BeamFormer (CBF) for jointly performing denoising, dereverberation, and source separation (DN+DR+SS) in a computationally efficient way. Conventionally, a cascade configuration, composed of a Weighted Prediction Error minimization (WPE) dereverberation filter followed by a Minimum Variance Distortionless Response (MVDR) beamformer, has been used as the state-of-the-art frontend of far-field speech recognition, even though this approach's overall optimality is not guaranteed. In the blind signal processing area, an approach for jointly optimizing dereverberation and source separation (DR+SS) has been proposed; however, it requires huge computing cost, and has not been extended for applications to DN+DR+SS. To overcome the above limitations, this paper develops new approaches for jointly optimizing DN+DR+SS in a computationally much more efficient way. To this end, we first present an objective function to optimize a CBF for performing DN+DR+SS based on maximum likelihood estimation on an assumption that the steering vectors of the target signals are given or can be estimated, e.g., using a neural network. This paper refers to a CBF optimized by this objective function as a weighted Minimum-Power Distortionless Response (wMPDR) CBF. Then, we derive two algorithms for optimizing a wMPDR CBF based on two different ways of factorizing a CBF into WPE filters and beamformers: one based on an extension of the conventional joint optimization approach proposed for DR+SS and another based on a novel technique. Experiments using noisy reverberant sound mixtures show that the proposed optimization approaches greatly improve the performance of the speech enhancement in comparison with the conventional cascade configuration in terms of signal distortion measures and ASR performance. The proposed approaches also greatly reduce the computing cost with improved estimation accuracy in comparison with the conventional joint optimization approach.

Jointly Optimal Denoising, Dereverberation, and Source Separation