We consider the general problem of microphone array signal processing in diffuse noise environments. This has various applications epitomized by speech enhancement and robust Automatic Speech Recognition (ASR) for microphone arrays. Diffuse noise arriving from almost all directions is often encountered in the real world, and has been one of the major obstacles against successful application of existing noise suppression and Direction-Of-Arrival (DOA) estimation techniques. We operate in the time-frequency domain, where signal and noise are assumed to be zero-mean Gaussian and modeled by their respective covariance matrices. Firstly, we introduce a general linear subspace model of the noise covariance matrix that extends three state-of-the-art models, and introduce a fourth more flexible real-valued noise covariance model. We experimentally assess the fit of each model to real-world noise. Secondly, we apply this general model to the task of diffuse noise suppression with a known target steering vector. In the state-of-the-art Wiener post-filtering approach, it is essential to accurately estimate the target power spectrogram. We propose a unified estimation framework applicable to the general noise model, which is based on projecting the observed covariance matrix onto the orthogonal complement of the noise model subspace. Ideally, this projection is noise-free, and enables accurate estimation of the target power spectrogram. The proposed framework for noise suppression is assessed through experiments with realworld noise. Thirdly, we address the task of DOA estimation of multiple sources. The performance of the state-of-the-art MUltiple SIgnal Classification (MUSIC) algorithm is known to degrade in the presence of diffuse noise. In order to mitigate this effect, we estimate the signal covariance matrix and subsequently apply MUSIC to it. The estimation relies on the abovementioned noise-free component of the observed covariance matrix and on the reconstruction of the remaining component belonging to the noise subspace. We design two alternative algorithms based on low-rank matrix completion and trace-norm minimization that exploit the low-rankness and the positive semidefiniteness of the signal covariance matrix. The performance of the proposed method with each noise model was compared using a large database we created. Finally, we present a unified framework applicable to the general noise model for diffuse noise suppression with an unknown target steering vector. This is important for effective noise suppression in the real-world, because the steering vector is usually not accurately known in practice. We jointly estimate the target steering vector and the target power spectrogram for designing the beamformer and the Wiener post-filter. The estimation is based on rank-1 completion and Principal Component Analysis (PCA). The proposed framework is shown to enable more effective noise suppression improving the SNR by about 7dB, compared to the state-of-the-art Independent Vector Analysis (IVA).
