New Approaches for Speech Enhancement in the Short-Time Fourier Transform Domain

Speech enhancement aims at the improvement of speech quality by using various algorithms. A speech enhancement technique can be implemented as either a time domain or a transform domain method. In the transform domain speech enhancement, the spectrum of clean speech signal is estimated through the modification of noisy speech spectrum and then it is used to obtain the enhanced speech signal in the time domain. Among the existing transform domain methods in the literature, the short-time Fourier transform (STFT) processing has particularly served as the basis to implement most of the frequency domain methods. In general, speech enhancement methods in the STFT domain can be categorized into the estimators of complex discrete Fourier transform (DFT) coefficients and the estimators of real-valued short-time spectral amplitude (STSA). Due to the computational efficiency of the STSA estimation method and also its superior performance in most cases, as compared to the estimators of complex DFT coefficients, we focus mostly on the estimation of speech STSA throughout this work and aim at developing algorithms for noise reduction and reverberation suppression. First, we tackle the problem of additive noise reduction using the single-channel Bayesian STSA estimation method. In this respect, we present new schemes for the selection of Bayesian cost function parameters for a parametric STSA estimator, namely the W�-SA estimator, based on an initial estimate of the speech and also the properties of human auditory system. We further use the latter information to design an efficient flooring scheme for the gain function of the STSA estimator. Next, we apply the generalized Gaussian distribution (GGD) to theW�-SA estimator as the speech STSA prior and propose to choose its parameters according to noise spectral variance and a priori signal to noise ratio (SNR). The suggested STSA estimation schemes are able to provide further noise reduction as well as less speech distortion, as compared to the previous methods. Quality and noise reduction performance evaluations indicated the superiority of the proposed speech STSA estimation with respect to the previous estimators. Regarding the multi-channel counterpart of the STSA estimation method, first we generalize the proposed single-channel W�-SA estimator to the multi-channel case for spatially uncorrelated noise. It is shown that under the Bayesian framework, a straightforward extension from the single-channel to the multi-channel case can be performed by generalizing the STSA estimator parameters, i.e. � and �. Next, we develop Bayesian STSA estimators by taking advantage of speech spectral phase rather than only relying on the spectral amplitude of observations, in contrast to conventional methods. This contribution is presented for the multi-channel scenario with single-channel as a special case. Next, we aim at developing multi-channel STSA estimation under spatially correlated noise and derive a generic structure for the extension of a single-channel estimator to its multi-channel counterpart. It is shown that the derived multi-channel extension requires a proper estimate of the spatial correlation matrix of noise. Subsequently, we focus on the estimation of noise correlation matrix, that is not only important in the multi-channel STSA estimation scheme but also highly useful in different beamforming methods. Next, we aim at speech reverberation suppression in the STFT domain using the weighted prediction error (WPE) method. The original WPE method requires an estimate of the desired speech spectral variance along with reverberation prediction weights, leading to a sub-optimal strategy that alternatively estimates each of these two quantities. Also, similar to most other STFT based speech enhancement methods, the desired speech coefficients are assumed to be temporally independent, while this assumption is inaccurate. Taking these into account, first, we employ a suitable estimator for the speech spectral variance and integrate it into the estimation of the reverberation prediction weights. In addition to the performance advantage with respect to the previous versions of the WPE method, the presented approach provides a good reduction in implementation complexity. Next, we take into account the temporal correlation present in the STFT of the desired speech, namely the inter-frame correlation (IFC), and consider an approximate model where only the frames within each segment of speech are considered as correlated. Furthermore, an efficient method for the estimation of the underlying IFC matrix is developed based on the extension of the speech variance estimator proposed previously. The performance results reveal lower residual reverberation and higher overall quality provided by the proposed method. Finally, we focus on the problem of late reverberation suppression using the classic speech spectral enhancement method originally developed for additive noise reduction. As our main contribution, we propose a novel late reverberant spectral variance (LRSV) estimator which replaces the noise spectral variance in order to modify the gain function for reverberation suppression. The suggested approach employs a modified version of the WPE method in a model based smoothing scheme used for the estimation of the LRSV. According to the experiments, the proposed LRSV estimator outperforms the previous major methods considerably and scores the closest results to the theoretically true LRSV estimator. Particularly, in case of changing room impulse responses (RIRs) where other methods cannot follow the true LRSV estimator accurately, the suggested estimator is able to track true LRSV values and results in a smaller tracking error. We also target a few other aspects of the spectral enhancement method for reverberation suppression, which were explored before only for the purpose of noise reduction. These contributions include the estimation of signal to reverberant ratio (SRR) and the development of new schemes for the speech presence probability (SPP) and spectral gain flooring in the context of late reverberation suppression.