GSVD-based optimal filtering for single and multimicrophone speech enhancement

A class of SVD-based signal enhancement procedures is described, which amount to a specific optimal filtering technique for the case where the so-called 'desired response' signal cannot be observed. It is shown that this optimal filter can be written as a function of the generalized singular vectors and singular values of a so-called speech and noise data matrix. A number of simple symmetry properties of the optimal filter are derived, which are valid for the white noise case as well as for the coloured noise case. Also the averaging step of the standard one-microphone SVD-based noise reduction techniques is investigated, leading to serious doubts about the necessity of this averaging step. When applying this technique for multi-microphone noise reduction, it is shown that for simple scenarios, where we consider localised sources and no multipath propagation, this technique exhibits some kind of beamforming behaviour. We further compare the performance of this technique with standard beamforming techniques, showing that for all reverberation times the performance of the SVD-based optimal filter is better than beamforming.

We present a generalized singular value decomposition (GSVD) based multi-user (MU) multi-stream multiple-input multiple-output (MIMO) precoding scheme with limited feedback. Our precoding scheme maximizes the signal to leakage and noise ratio (SLNR), so that it does not require any iterations to obtain precoding matrices. However, in MU-MIMO system, the precoding matrix should be computed at transmit side, because the precoding matrix of a user affects those of other users. Accordingly, full channel state information (CSI) for all users is required at the transmitter, which prevents MU-MIMO precoding implementable. To overcome this problem, an efficient limited feedback algorithm optimized to the GSVD based MU-MIMO precoding is proposed. Here, by extracting the parameters to be utilized in GSVD based precoding from the full CSI, the amount of feedback information is reduced. Furthermore, by analyzing their statistical properties, the parameters are efficiently quantized according to their probability densities. Finally, we develop a modified GSVD based precoding considering the channel quantization errors due to the limited feedback.

A method for eigenvalue localization for discrete-time systems which does not require explicit placement of the closed-loop eigenvalues is presented. The method is based on a simultaneous diagonalization accomplished by means of the generalized singular value decomposition (GSVD). The GSVD is introduced and applied to the system matrix and modified control distribution matrix to show that a proper choice of the full state feedback gain matrix leads to a diagonalized closed-loop system matrix. Furthermore, there exists a particular choice of the feedback gain matrix which reduces the closed-loop singular values as compared with those of the open loop. This fact is used to suggest an iterative algorithm for localization of the closed-loop eigenvalues. >

Abstract. The electron density distribution of the low- and mid-latitude ionosphere has been investigated by the computerized tomography technique using a Generalized Singular Value Decomposition (GSVD) based algorithm. Model ionospheric total electron content (TEC) data obtained from the International Reference Ionosphere 2001 and slant relative TEC data measured at a chain of three stations receiving transit satellite transmissions in Alaska, USA are used in this analysis. The issue of optimum efficiency of the GSVD algorithm in the reconstruction of ionospheric structures is being addressed through simulation of the equatorial ionization anomaly (EIA), in addition to its application to investigate complicated ionospheric density irregularities. Results show that the Generalized Cross Validation approach to find the regularization parameter and the corresponding solution gives a very good reconstructed image of the low-latitude ionosphere and the EIA within it. Provided that some minimum norm is fulfilled, the GSVD solution is found to be least affected by considerations, such as pixel size and number of ray paths. The method has also been used to investigate the behaviour of the mid-latitude ionosphere under magnetically quiet and disturbed conditions.

In this paper we examine the use of generalized singular value decomposition (GSVD) for coordinated beamforming in MIMO systems. GSVD facilitates joint decomposition of a class of matrices arising inherently in source-to-2 destination MIMO broadcast scenarios. GSVD allows two channels of suitable dimensionality to be jointly diagonalized, i.e. to be reduced to non-interfering virtual broadcast channels, through the use of jointly determined transmit precoding and receiver reconstruction matrices. Potential applications for GSVD-based beamforming can be found in MIMO broadcasting, as well as in MIMO relaying under all amplify-and-forward, decode-and-forward, and code-and-forward relay processing schemes. Several of them are highlighted here. We also present simulation-based performance analysis results to justify the use of GSVD for coordinated beamforming.

In this paper, a general framework of the multiple- input multiple-output (MIMO) transceiver design for 5G multiple access (5GMA), including both non- orthogonal multiple access (NOMA) and sparsity code multiple access (SCMA), is developed to enhance the system throughput of next generation of communication systems. By applying generalized singular value decomposition (GSVD), MIMO channels can be decomposed into multiple single-input single- output (SISO) channels, to which the concept of NOMA and SCMA can ideally be applied. GSVD based precoding is proposed to both uplink and downlink 5GMA transmissions, and simulation results are provided to demonstrate the performance of the proposed schemes.

In this paper, we propose a new Multilinear Generalized Singular Value Decomposition (ML-GSVD) which allows to jointly factorize a set of matrices with one common dimension. The ML-GSVD is an extension of the Generalized Singular Value Decomposition (GSVD) for more than two matrices. In comparison with other approaches that extend the GSVD, the proposed tensor decomposition preserves the essential properties of the original GSVD, such as orthogonality of the second mode factor matrices. In this work, we introduce two algorithms to compute the ML-GSVD. In addition, we present an application of the ML-GSVD to compute the beamforming matrices for the multi-user MIMO downlink channel with more than two users in wireless communications.

Noise reduction for speech applications is often formulated as a digital filtering problem, where the clean speech estimate is obtained by passing the noisy speech through a linear filter/transform. With such a formulation, the core issue of noise reduction becomes how to design an optimal filter (based on the statistics of the speech and noise signals) that can significantly suppress noise without introducing perceptually noticeable speech distortion. The optimal filters can be designed either in the time or in a transform domain. The advantage of working in a transform space is that, if the transform is selected properly, the speech and noise signals may be better separated in that space, thereby enabling better filter estimation and noise reduction performance. Although many different transforms exist, most efforts in the field of noise reduction have been focused only on the Fourier and Karhunen-Loeve transforms. Even with these two, no formal study has been carried out to investigate which transform can outperform the other. In this paper, we reformulate the noise reduction problem into a more generalized transform domain. We will show some of the advantages of working in this generalized domain, such as 1) different transforms can be used to replace each other without any requirement to change the algorithm (optimal filter) formulation, and 2) it is easier to fairly compare different transforms for their noise reduction performance. We will also address how to design different optimal and suboptimal filters in such a generalized transform domain.

A speech analyzer is described which measures the degree of fit between the energy distribution of any speech signal and a set of “standard” energy distribution patterns stored in the machine. This technique is based on the assumption that a phoneme can be characterized, at least for a single speaker, by specifying the points of energy concentration in the frequency spectrum and by specifying the energy envelope, i.e., energy vs time characteristic, of selected portions of the spectrum. A set of contiguous band filters covering the frequency range 100–7000 cycles/sec are used in combination with rectifiers and integrators to produce polarized signals which are functions of the energy distribution of the speech input signal. Improved selectivity and discrimination against noise and noise-like signals are obtained by combining the outputs from adjacent filters to measure the difference between signal levels, and further combining signals to measure the second difference between signals in adjacent filter bands. “Optimum filters” for phonemes are constructed by adding output signals corresponding to frequencies of energy concentration and subtracting signals corresponding to energy minima; this summation generates a signal proportional to the degree of “fit” between the speech signal and the specified pattern. Separate summations of the low and high frequency filter outputs provide measures of intensity, voiced-unvoiced detection, and pitch extraction signals. Some results are presented.

Speech can be expressed as a mechanism of expressing thoughts and ideas using vocal sounds. In humans, speech signals are generated at vocal cords, travelled through the vocal tract, and finally produced & transmitted through speaker’s mouth. These speech signals then usually travels through air or other mediums to the listener’s ear, where it acts as pressure waves. The bandwidth of speech signal is around 4 KHz. The noise produced by various ambient sources such as vehicles normally lies in this frequency range. Therefore, speech signals get easily distorted by the ambient noise. These distorted or degraded speech signals are called noisy speech signals. This paper focuses on speech processing (in particularly speech enhancement) of the noisy speech signals. This is very important as speech is the most commonly used way of communication and interaction between humans; however, it is very complex to understand. Therefore, this paper proposes an adaptive algorithm based on Wiener filter for speech enhancement. The proposed adaptive Wiener filter depends on the adaptation of the filter transfer function from sample to sample based on the speech signal statistics (mean and variance). The adaptive Wiener filter is implemented in time domain rather than in frequency domain. This is done to accommodate the random speech signal. The proposed method is compared to the traditional Wiener filter and the spectral subtraction methods.

Memory-based collaborative filtering (CF) aims at predicting the rating of a certain item for a particular user based on the previous ratings from similar users and/or similar items. Previous studies in finding similar users and items have several drawbacks. First, they are based on user-defined similarity measurements, such as Pearson Correlation Coefficient (PCC) or Vector Space Similarity (VSS), which are, for the most part, not adaptive and optimized for specific applications and data. Second, these similarity measures are restricted to symmetric ones such that the similarity between A and B is the same as that for B and A, although symmetry may not always hold in many real world applications. Third, they typically treat the similarity functions between users and functions between items separately. However, in reality, the similarities between users and between items are inter-related. In this paper, we propose a novel unified model for users and items, known as Similarity Learning based Collaborative Filtering (SLCF) , based on a novel adaptive bidirectional asymmetric similarity measurement. Our proposed model automatically learns asymmetric similarities between users and items at the same time through matrix factorization. Theoretical analysis shows that our model is a novel generalization of singular value decomposition (SVD). We show that, once the similarity relation is learned, it can be used flexibly in many ways for rating prediction. To take full advantage of the model, we propose several strategies to make the best use of the proposed similarity function for rating prediction. The similarity can be used either to improve the memory-based approaches or directly in a model based CF approaches. In addition, we also propose an online version of the rating prediction method to incorporate new users and new items. We evaluate SLCF using three benchmark datasets, including MovieLens, EachMovie and Netflix, through which we show that our methods can outperform many state-of-the-art baselines.

How to effectively extract fault features from noisy vibration signals is a key problem to be solved in bearing fault diagnosis. The difficulty here mainly lies in the fact that the components of interest are almost submerged by background noise and external interference. To accurately implement extraction of fault features, nuclear norm minimization (NNM) has been introduced to fault feature extraction due to its powerful denoising capability. However, NNM treats all singular values equally, which may result in components of interest with small singular values being abandoned, especially when a bearing defect is at its incipient stage. Therefore, to enhance the flexibility and effectiveness of NNM in handling practical problems, fault information-oriented weighted nuclear norm minimization (FIWNNM) is proposed for extracting bearing fault features, in which singular values are treated differently by assigning appropriate weights according to the physical meanings. Through the proposed FIWNNM, fault features can be drawn from a noisy signal, even when contaminated by strong noise and external interferences. The analysis results from both simulated and real measured signals are used as the verification of the proposed FIWNNM.

A speech enhancement system for noisy speech signals under different environments, namely airport, babble, car, exhibition, restaurant, station, street and train, is designed and implemented in this paper. Spectral subtraction is the most popular method for speech enhancement which suffers from perceptually annoying musical noise. Musical noise is reduced here by using low variance spectrum estimators and enhancement is achieved by wavelet thresholding the multitaper spectrum of the speech. The main feature of the proposed system is a novel switching mechanism to an optimal wavelet filter bank or wavelet packet filter bank matching to the critical bands of the human ear, based on the type of noise present in the input speech. The system is evaluated using noisy speech signals under different environment noises at different signal to noise ratios. The subjective and objective test results show that the proposed method improves the quality and intelligibility of speech signals.

Noise estimation and suppression is very important for improving the quality of speech signal. Noises exist in almost all places. In reality, more than one noise degrades the speech signal. It is hard to find and supress various types of noise that affect the speech quality. This paper proposed a method for noise estimation of mixed non-stationary noisy speech signal. This method uses Spectral properties of the noisy speech signal to detect the frequency regions of noise signal. Highest frequency of speech signal is calculated and it is considered as the threshold value for separating noise signal and clean speech signal. Using Spectral subtraction, Standard deviation of noise spectrum is subtracted with noisy spectrum to acquire enhanced speech signal. Performance of the method is evaluated using SNR and Spectrogram. The main focus of this paper is to propose an independent method which estimates the noise of any type and nature.

A novel approach for multimicrophone speech dereverberation is presented. The method is based on the construction of the null subspace of the data matrix in the presence of colored noise, using the generalized singular-value decomposition (GSVD) technique, or the generalized eigenvalue decomposition (GEVD) of the respective correlation matrices. The special Silvester structure of the filtering matrix, related to this subspace, is exploited for deriving a total least squares (TLS) estimate for the acoustical transfer functions (ATFs). Other less robust but computationally more efficient methods are derived based on the same structure and on the QR decomposition (QRD). A preliminary study of the incorporation of the subspace method into a subband framework proves to be efficient, although some problems remain open. Speech reconstruction is achieved by virtue of the matched filter beamformer (MFBF). An experimental study supports the potential of the proposed methods.