Deep learning for minimum mean-square error approaches to speech enhancement

Minimum mean-square error (MMSE) approaches to speech enhancement are widely used in the literature. The quality of enhanced speech produced by an MMSE approach is directly impacted by the accuracy of the employed a priori signal-to-noise ratio (SNR) estimator. In this paper, the a priori SNR estimate spectral distortion (SD) level that results in a just-noticeable difference (JND) in the perceived quality of MMSE approach enhanced speech is found. The JND SD level is indicative of the accuracy that an a priori SNR estimator must exceed to have no impact on the perceived quality of MMSE approach enhanced speech. To measure the JND SD level, listening tests are conducted across five SNR levels, five noise sources, and two MMSE approaches [the MMSE short-time spectral amplitude (MMSE-STSA) estimator and the Wiener filter]. A statistical analysis of the results indicates that the JND SD level increases with the SNR level, is higher for the MMSE-STSA estimator, and is not impacted by the type of background noise. Following the literature, a significant improvement in a priori SNR estimation accuracy is required to reach the JND SD level.

Speech corrupted by background noise (or noisy speech) can cause misinterpretation and fatigue during phone and conference calls, and for hearing aid users. Noisy speech can also severely impact the performance of speech processing systems such as automatic speech recognition (ASR), automatic speaker verification (ASV), and automatic speaker identification (ASI) systems. Currently, deep learning approaches are employed in an end-to-end fashion to improve robustness. The target speech (or clean speech) is used as the training target or large noisy speech datasets are used to facilitate multi-condition training. In this dissertation, we propose competitive alternatives to the preceding approaches by updating two classic robust speech processing techniques using deep learning. The two techniques include minimum mean-square error (MMSE) and missing data approaches. An MMSE estimator aims to improve the perceived quality and intelligibility of noisy speech. This is accomplished by suppressing any background noise without distorting the speech. Prior to the introduction of deep learning, MMSE estimators were the standard speech enhancement approach. MMSE estimators require the accurate estimation of the a priori signal-to-noise ratio (SNR) to attain a high level of speech enhancement performance. However, current methods produce a priori SNR estimates with a large tracking delay and a considerable amount of bias. Hence, we propose a deep learning approach to a priori SNR estimation that is significantly more accurate than previous estimators, called Deep Xi. Through objective and subjective testing across multiple conditions, such as real-world non-stationary and coloured noise sources at multiple SNR levels, we show that Deep Xi allows MMSE estimators to produce the highest quality enhanced speech amongst all clean speech magnitude spectrum estimators. Missing data approaches improve robustness by performing inference only on noisy speech features that reliably represent clean speech. In particular, the marginalisation method was able to significantly increase the robustness of Gaussian mixture model (GMM)-based speech classification systems (e.g. GMM-based ASR, ASV, or ASI systems) in the early 2000s. However, deep neural networks (DNNs) used in current speech classification systems are non-probabilistic, a requirement for marginalisation. Hence, multi-condition training or noisy speech pre-processing is used to increase the robustness of DNN-based speech classification systems. Recently, sum-product networks (SPNs) were proposed, which are deep probabilistic graphical models that can perform the probabilistic queries required for missing data approaches. While available toolkits for SPNs are in their infancy, we show through an ASI task that SPNs using missing data approaches could be a strong alternative for robust speech processing in the future. This dissertation demonstrates that MMSE estimators and missing data approaches are still relevant approaches to robust speech processing when assisted by deep learning.

An interference cancellation scheme for CDMA communication systems is presented. The algorithm is based on constrained optimization where receiver output power is minimized subject to the constraint that a desired code be passed with no distortion. Output power minimization (OPM) schemes have been shown to be equivalent to minimum mean square error (MMSE) approaches. Like MMSE approaches, OPM schemes do not require explicit knowledge of the interference structure. Unlike most MMSE approaches, however, OPM schemes do not require training. The algorithms are blind in the sense that only knowledge of the desired user's code (not the actual transmitted bit sequence) and associated timing is necessary. Moreover, the algorithms are linear and, therefore, not susceptible to misconvergence. The particular OPM implementation presented is based on the generalized sidelobe canceller structure which was originally developed for adaptive cancellation of spatial interference in array signal processing applications. Algorithm performance results are presented in the form of signal to interference ratios and bit error rate curves.

LSTM-convolutional-BLSTM encoder-decoder network for minimum mean-square error approach to speech enhancement

Presently, because of the development of deep learning technology, there has been increasingly more attention on state-of-the-art masking and mapping based speech enhancement methods. However, traditional speech enhancement approaches, like minimum mean-square error (MMSE) and wiener filter (WF) have not been fully investigated. In order to the better characterize, we proposed a deep learning based MMSE approach for single-channel speech enhancement based on Non-negative Matrix Factorization (NMF). The performance of MMSE approach can be improved by a priori signal-to-noise ratio. Therefore, we utilized an NMF-based Densely Connected Convolutional Network (DenseNet) as an estimator of the a priori signal-to-noise ratio (SNR). In test stage, multiple SNR level speech from colored noise sources and real-world non-stationary noise sources were used for evaluation. As expected, our present study outperformed many previous speech enhancement methods.

Speech enhancement based on β-order MMSE estimation of Short Time Spectral Amplitude and Laplacian speech modeling

An important issue in Wyner-Ziv video coding is the reconstruction of Wyner-Ziv frames with decoded bit-planes. So far, there are two major approaches: the Maximum a Posteriori (MAP) reconstruction and the Minimum Mean Square Error (MMSE) reconstruction algorithms. However, these approaches do not exploit smoothness constraints in natural images. In this paper, we model a Wyner-Ziv frame by Markov random fields (MRFs), and produce reconstruction results by finding an MAP estimation of the MRF model. In the MRF model, the energy function consists of two terms: a data term, MSE distortion metric in this paper, measuring the statistical correlation between side-information and the source, and a smoothness term enforcing spatial coherence. In order to better describe the spatial constraints of images, we propose a context-adaptive smoothness term by analyzing the correspondence between the output of Slepian-Wolf decoding and successive frames available at decoders. The significance of the smoothness term varies in accordance with the spatial variation within different regions. To some extent, the proposed approach is an extension to the MAP and MMSE approaches by exploiting the intrinsic smoothness characteristic of natural images. Experimental results demonstrate a considerable performance gain compared with the MAP and MMSE approaches.

This paper provides a new approach to solve the handover problem in high mobility cellular communication networks. In particular, the mobile node, e.g, the high-speed train(HST), is equipped with multiple antennas by which it finds the target base station (BS) quickly with only receive beamforming. When only imperfect channel state information (CSI) is available, the output signal-to-noise ratio (SNR) of the receive beamformer will be interfered by signals from different nearby BSs, which may lead to possible error in the selection of target BS. To deal with this, two methods, i.e., maximum-ratio combining (MRC) and Minimum Mean Square Error (MMSE), are proposed to obtain the optimal beamforming vectors. Simulation results show that both the proposed methods perform well, and the MMSE approach has good robustness.

In this paper, we provide a theoretical analysis of the minimum mean-square error short-time spectral amplitude (MMSE-STSA) estimator with the biased a priori SNR estimation and its extension to musical-noise-free speech enhancement. Recently, musical-noise-free speech enhancement has been proposed, where no musical noise is generated in iterative spectral subtraction. However, no existence of the musical-noise-free condition in the MMSE-STSA estimator has been reported. Therefore, in this paper, we show that the musical-noise-free condition exists in the biased MMSE-STSA estimator via the theoretical analysis. In addition, we perform comparative experiments and clarify the efficacy of the proposed musical-noise-free speech enhancement.

In this paper, a Dirty Paper Coding (DPC) based Minimum Mean Square Error (MMSE) beamforming design for a MIMO interference channel has been introduced. It includes signal leakage and linear transmit filters. At each transmitter, MMSE approach has been used comprising the signal with the interference. The simulation results show that the proposed design achieves significant reduction in mean square error (MSE) value as compared to leakage based MMSE approach. An optimal DPC strategy has been used for cancelling causal interference.

We present a low-complexity equalizer for multicarrier code-division multiple-access (MC-CDMA) downlink systems over time-varying (TV) multipath channels with non-negligible Doppler spread. The equalization algorithm, which is based on a block minimum mean-squared error (MMSE) approach, exploits the band structure of the frequency-domain channel matrix by means of a band LDL/sup H/ factorization. The complexity of the proposed block MMSE equalizer is linear in the number of subcarriers, and smaller with respect to a serial MMSE equalizer characterized by a similar performance.

For the code division multiple access (CDMA) downlink channel, the chip-level equalization has been considered in this paper. There is no interference after despreading if all spreading codes are orthogonal, as in IS-95. However, it cannot be true for a frequency-selective fading channel. In this case, the chip-level equalization can be applied to restore the orthogonality. We investigate the chip-level equalization using finite impulse response (FIR) equalizers for the mobile station with multiple receive antennas. A blind approach and the minimum mean square error (MMSE) approach with code-multiplexed pilot are considered. A generalized MMSE equalization, which combines the MMSE and blind approaches together, is also investigated. It is shown that the generalized MMSE equalizer can effectively increase the number of samples to track the variation of channel and thereby performs better when the coherence time is small. In addition, we derive closed-form solutions of the blind, MMSE, and generalized MMSE equalizers for given channels.

This reported work focuses on weighted sum-rate maximisation (WSRM) of cognitive radio ad-hoc networks, where a K user multiple-input multiple-output interference network (K-MIMO-IFN) uses the same spectrum with a licenced primary user. Because the WSRM problem in K-MIMO-IFN is non-convex and it is difficult to get an optimal solution directly, the weighted minimum mean square error (MMSE) approach is used to make the problem easier to handle. This report then proposes a dual-MMSE-algorithm, which iteratively finds a local optimal solution and only needs the local channel knowledge. Simulation results show that the proposed algorithm outperforms other conventional algorithms.

Interpolation filtering in digital demodulators with fixed input sampling rate is treated. The procedures for optimum interpolation filter design which account for the peculiarities of the digital demodulators are presented. Minimum mean square error (MMSE) interpolation filters are discussed, and a design procedure for standard input signals is given. For some hardwired implementations the on-line computation of the filter coefficients can be advantageous. For those cases, the MMSE approach is almost infeasible and polynomial approximations are used. New design algorithms for coefficient computation for optimum polynomial interpolators are given. The design procedure is illustrated by a number of examples, and the results are compared to the nonpolynomial MMSE case. >

In this paper, we address theoretical studies on the existence of musical-noise-free conditions for statistical-model-based speech enhancement methods. Recently, musical-noise-free speech enhancement has been proposed, where no musical noise is generated in iterative spectral subtraction, iterative Wiener filtering, and the minimum mean-square error short-time spectral amplitude (MMSE-STSA) estimator. As an extension of this theory to more flexible speech enhancement algorithms, in this paper, we reveal that the musical-noise-free condition exists in the methods with the a priori statistical speech models, e.g., the biased generalized MMSE-STSA estimator, via higher-order-statistics analysis. In addition, we perform comparative experiments and clarify the efficacy of the proposed musical-noise-free speech enhancement.