Computationally effective algorithm for robust weighted averaging

One of the greatest disadvantages of the weighted signal averaging method is its sensitivity to the presence of noise and outliers in data and the need to estimate the noise variance in all signal cycles. The robust weighted averaging method based on the epsilon-insensitive loss function is free of these disadvantages, but has a very high computational burden and requires a choice of the insensitivity parameter epsilon. In this study, a new computationally effective algorithm for robust weighted averaging with automatic adjustment of the insensitivity parameter is introduced.     

Robust deconvolution of deterministic and random signals

We consider the problem of designing an estimation filter to recover a signal x[n] convolved with a linear time-invariant (LTI) filter h[n] and corrupted by additive noise. Our development treats the case in which the signal x[n] is deterministic and the case in which it is a stationary random process. Both formulations take advantage of some a priori knowledge on the class of underlying signals. In the deterministic setting, the signal is assumed to have bounded (weighted) energy; in the stochastic setting, the power spectra of the signal and noise are bounded at each frequency. The difficulty encountered in these estimation problems is that the mean-squared error (MSE) at the output of the estimation filter depends on the problem unknowns and therefore cannot be minimized. Beginning with the deterministic setting, we develop a minimax MSE estimation filter that minimizes the worst case point-wise MSE between the true signal x[n] and the estimated signal, over the class of bounded-norm inputs. We then establish that the MSE at the output of the minimax MSE filter is smaller than the MSE at the output of the conventional inverse filter, for all admissible signals. Next we treat the stochastic scenario, for which we propose a minimax regret estimation filter to deal with the power spectrum uncertainties. This filter is designed to minimize the worst case difference between the MSE in the presence of power spectrum uncertainties, and the MSE of the Wiener filter that knows the correct power spectra. The minimax regret filter takes the entire uncertainty interval into account, and as demonstrated through an example, can often lead to improved performance over traditional minimax MSE approaches for this problem     

GSVD-based optimal filtering for single and multimicrophone speech enhancement

A generalized singular value decomposition (GSVD) based algorithm is proposed for enhancing multimicrophone speech signals degraded by additive colored noise. This GSVD-based multimicrophone algorithm can be considered to be an extension of the single-microphone signal subspace algorithms for enhancing noisy speech signals and amounts to a specific optimal filtering problem when the desired response signal cannot be observed. The optimal filter can be written as a function of the generalized singular vectors and singular values of a speech and noise data matrix. A number of symmetry properties are derived for the single-microphone and multimicrophone optimal filter, which are valid for the white noise case as well as for the colored noise case. In addition, the averaging step of some single-microphone signal subspace algorithms is examined, leading to the conclusion that this averaging operation is unnecessary and even suboptimal. For simple situations, where we consider localized sources and no multipath propagation, the GSVD-based optimal filtering technique exhibits the spatial directivity pattern of a beamformer. When comparing the noise reduction performance for realistic situations, simulations show that the GSVD-based optimal filtering technique has a better performance than standard fixed and adaptive beamforming techniques for all reverberation times and that it is more robust to deviations from the nominal situation, as, e.g., encountered in uncalibrated microphone arrays.     

Adaptive filter for event-related bioelectric signals using animpulse correlated reference input: comparison with signal averagingtechniques

Many bioelectric signals result from the electrical response of physiological systems to an impulse that can be internal (ECG signals) or external (evoked potentials). In this paper an adaptive impulse correlated filter (AICF) for event-related signals that are time-locked to a stimulus is presented. This filter estimates the deterministic component of the signal and removes the noise uncorrelated with the stimulus, even if this noise is colored, as in the case of evoked potentials. The filter needs two inputs: the signal (primary input) and an impulse correlated with the deterministic component (reference input). We use the LMS algorithm to adjust the weights in the adaptive process. First, we show that the AICF is equivalent to exponentially weighted averaging (EWA) when using the LMS algorithm. A quantitative analysis of the signal-to-noise ratio improvement, convergence, and misadjustment error is presented. A comparison of the AICF with ensemble averaging (EA) and moving window averaging (MWA) techniques is also presented. The adaptive filter is applied to real high-resolution ECG signals and time-varying somatosensory evoked potentials.     

基于混沌与高阶累积量的微弱信号检测

针对微弱信号幅值很小,常被噪声淹没,而传统去噪方法效果并不理想,研究基于混沌与高阶累积量的微弱正弦信号检测方法,建立仿真模型,并将最大李雅普诺夫Lyapunov指数作为判断混沌系统相变的量化依据．自动识别混沌系统的临界状态,从而准确确定系统的策动力临界闽值。仿真实验表明该方法能有效检测出淹没在高斯噪声中的微弱正弦信号,检测信噪比为-37dB时,幅度检测相对误差为1．9％。该方法幅度检测门限低,具有广泛应用前景。     

Interpolation of signals with missing data using Principal Component Analysis

A non-iterative methodology for the interpolation and regularization of multidimensional sampled signals with missing data resorting to Principal Component Analysis (PCA) is introduced. Based on unbiased sub-optimal estimators for the mean and covariance of signals corrupted by zero-mean noise, the PCA is performed and the signals are interpolated and regularized. The optimal solution is obtained from a weighted least mean square minimization problem, and upper and lower bounds are provided for the mean square interpolation error. This solution is a refinement to a previously introduced method proposed by the author Oliveira (Proceedings of the IEEE international conference on acoustics, speech, and signal processing—ICASSP06, Toulouse, France, 2006), where three extensions are exploited: (i) mean substitution for covariance estimation, (ii) Tikhonov regularization method and, (iii) dynamic principal components selection. Performance assessment benchmarks relative to averaging, Papoulis-Gerchberg, and Power Factorization methods are included, given the results obtained from a series of Monte Carlo experiments with 1-D audio and 2-D image signals. Tight upper and lower bounds were observed, and improved performance was attained for the refined method. The generalization to multidimensional signals is immediate.     

空间相关色噪声下基于酉变换的信号源数目估计

空间相关色噪声环境下的信号源数目的估计一直是个难题.本文在窄带信号条件下,利用信号的时间相关长度大于噪声的时间相关长度这一事实,提出了一种色噪声环境下基于辅助变量和酉变换的信号源数目估计方法.构造适当的辅助变量减轻甚至消除噪声对检测性能的影响.对信号子空间和噪声子空间的正交性进行了分析得出新的估计准则.最后通过计算机仿真和实测数据对比已有的其他方法验证了本文方法的有效性和优越性.     

基于MPEG-AAC编码器的压缩域音频增强方法

本文基于MPEG-AAC音频编解码器,提出了一种压缩域的音频增强方法.首先,对含噪音频信号的比特流进行解码,得到含噪音频信号的MDCT系数;然后,利用修正的加权递归平均（Modified Weighted Recursive Averaging,MWRA）方法估计噪声功率;再者,利用基于听觉掩蔽原理的自适应β-阶双曲余弦（COSH）统计模型,对含噪音频的MDCT系数进行增强处理;最后,将增强后的MDCT系数重新量化编码,得到用于解码的增强比特流实验结果表明,本文提出的方法能有效去除AAC解码音频信号中的多种背景噪声,其性能明显优于参考方法.     

Signal detection in the presence of weakly dependent noise--I: Optimum detection

The problem of discrete-time signal detection in the presence of additive noise exhibiting a weak form of dependence is considered. A moving-average representation is used to model dependence in the noise sequence, and the degree of dependence is parameterized by the averaging weights. The weak-dependence model is then based on the situation in which terms depending to second or higher Order on the averaging weights can be considered to be negligible. Part I of this two-part study considers the problem of asymptotically efficient detection in this context for situations in which the noise statistics are known. An appropriate detector is sought by modifying the corresponding independent-noise detector structure in a way which does not increase detector complexity, and a corresponding weak-dependence design criterion is developed. The solution to this problem is then seen to be based on a linearly corrected version of the optimum independent-noise detection nonlinearity. The performance of this detector is compared to that of the corresponding optimum system for independent noise with the conclusion that performance gain is achieved by the proposed systems with no corresponding increase in complexity. Several specific examples are discussed to illustrate the types of noise environments for which this design technique is useful. Part II of this study will treat the problem of robust detection in the presence of weakly dependent noise.     

Robust L-estimation based forms of signal transforms and time-frequency representations

The L-estimation based signal transforms and time-frequency (TF) representations are introduced by considering the corresponding minimization problems in the Huber (1981, 1998) estimation theory. The standard signal transforms follow as the maximum likelihood solutions for the Gaussian additive noise environment. For signals corrupted by an impulse noise, the median-based transforms produce robust estimates of the non-noisy signal transforms. When the input noise is a mixture of Gaussian and impulse noise, the L-estimation-based signal transforms can outperform other estimates. In quadratic and higher order TF analysis, the resulting noise is inherently a mixture of the Gaussian input noise and an impulse noise component. In this case, the L-estimation-based signal representations can produce the best results. These transforms and TF representations give the standard and the median-based forms as special cases. A procedure for parameter selection in the L-estimation is proposed. The theory is illustrated and checked numerically.     

Design of partially adaptive array beamformers based on informationtheoretic criteria

In this paper, two basic problems in designing partially adaptive array beamformers based on the structure of generalized sidelobe canceller (GSC) are considered. The first problem is to decide the proper dimension of the required adaptive weight vector. Using the information of the array output power, we develop the detection formulas for the information theoretic criteria AIC and MDL to decide the proper dimension of the adaptive weight vector. If the input noise power is unknown a priori, efficient methods are proposed for estimating the input noise power in both cases, with and without the desired signal, to make the detection formulas still feasible. The second problem is to find the most appropriate channel signals for weight adaptation for efficiently canceling interference. An efficient method based on the maximum power reduction criterion is presented for selecting the most desired channel signals from the output of the signal blocking matrix. Theoretical analysis concerning the performance of the proposed methods is made. Computer simulations showing the effectiveness of the proposed methods are also provided     

Per‐antenna power minimization in symbol‐level precoding for the multibeam satellite downlink

This paper addresses the problem of multiuser interference in the forward downlink channel of a multibeam satellite system. A symbol‐level precoding scheme is considered, to exploit the multiuser interference and transform it into useful power at the receiver side, through a joint utilization of the data information and the channel state information. In this context, a per‐antenna power minimization scheme is proposed, under quality‐of‐service constraints, for multilevel modulation schemes. The consideration of the power limitations individually for each transmitting radio frequency chain is a central aspect of this work, and it allows to deal with systems using separate per‐antenna amplifiers. Moreover, this feature is also particularly relevant for systems suffering nonlinear effects of the channel. This is the case of satellite systems, where the nonlinear amplifiers should be properly driven to reduce the detrimental saturation effect. In the proposed scheme, the transmitted signals are designed to reduce the power peaks, while guaranteeing some specific target signal‐to‐noise ratios at the receivers. Numerical results are presented to show the effectiveness of the proposed scheme, which is compared both with the state of the art in symbol‐level precoding and with the conventional minimum mean square error precoding approach.     

Determination of amplitude levels of the piecewise constant signal by using polynomial approximation

A new approach to determining the amplitude levels of piecewise constant signal has been proposed that is based on using its multiplicative model and solving the problem of polynomial approximation. In case of the absence of noise, the statement of polynomial approximation problem is based on the requirement of exact match of the current signal value with the amplitude value of one of its levels. In case of the presence of ordinary additive noise, the problem statement is based on the least squares criterion, while the solution of problem is presented in the analytical form. For the case of the presence of pulse-type noise, the problem statement is based on the minimum duration criterion, while the problem solution is achieved numerically by an appropriate functional minimization in unknown amplitudes of levels. The case of binary piecewise constant signal is considered in detail. The results of numerical simulation are presented for the cases, where the binary signal is distorted by ordinary additive noise with Gaussian distribution law and the pulse-type noise with the Cauchy distribution law.     

A fuzzy clustering approach to EP estimation

The problem of extracting a useful signal (a response) buried in relatively high amplitude noise has been investigated, under the conditions of low signal-to-noise ratio. In particular, the authors present a method for detecting the “true” response of the brain resulting from repeated auditory stimulation, based on selective averaging of single-trial evoked potentials. Selective averaging: is accomplished in two steps. First, an unsupervised fuzzy-clustering algorithm is employed to identify groups of trials with similar characteristics, using a performance index as an optimization criterion. Then, typical responses are obtained by ensemble averaging of all trials in the same group. Similarity among the resulting estimates is quantified through a synchronization measure, which accounts for the percentage of time that the estimates are in phase. The performance of the classifier is evaluated with synthetic signals of known characteristics, and its usefulness is demonstrated with real electrophysiological data obtained from normal volunteers     

A novel phase congruency based algorithm for online data reduction in ambulatory EEG systems

Real signals are often corrupted by noise with a power spectrum variable over time. In applications involving these signals, it is expected that dynamically estimating and correcting for this noise would increase the amount of useful information extracted from the signal. One such application is scalp EEG monitoring in epilepsy, where electrical activity generated by cranio-facial muscles obscure the measured brainwaves. This paper presents a data-selection algorithm based on phase congruency to identify interictal spikes from background EEG; together with a novel statistical method that allows a more comprehensive trade-off based quantitative comparison of two algorithms which have been tested at a fixed threshold in the same database. Here, traditional phase congruency has been modified to incorporate a dynamic estimate of muscle activity present in the input scalp EEG signal. The proposed algorithm achieves 50% data reduction whilst detecting more than 80% of interictal spikes. This represents a significant improvement over the state-of-the-art denoising method for phase congruency.     

小波变换与匹配滤波耦合的激光雷达弱信号处理

远距离激光雷达回波信号弱,干扰强,处理比较困难。距离越远,得到的有用信号就越弱。为了提高激光雷达检测距离,对弱信号进行数字信号处理就显得很重要。采用一般方法常将干扰信号判断成有用信号,从而影响了激光雷达的工作能力。夺文采用小波变换和匹配滤波耦合的方法对激光雷达弱信号进行处理,既能从强噪声中提取有用信号,又能有效的去掉强干扰信号。采用一台TEA—CO2激光器进行实验,当采样速率达到200MHz时,对于信噪比大于1．2的含噪信号能有效地去掉噪声和强干扰信号,在保持原信号特征的情况下,准确地提取出有效的弱信号。这就有效地提高了激光雷达的工作能力。     

Spectrum Sensing Based on Deep Learning Classification for Cognitive Radios

Spectrum sensing is a key technology for cognitive radios.We present spectrum sensing as a classification problem and propose a sensing method based on deep learning classification.We normalize the received signal power to overcome the effects of noise power uncertainty.We train the model with as many types of signals as possible as well as noise data to enable the trained network model to adapt to untrained new signals.We also use transfer learning strategies to improve the performance for real-world signals.Extensive experiments are conducted to evaluate the performance of this method.The simulation results show that the proposed method performs better than two traditional spectrum sensing methods,i.e.,maximum-minimum eigenvalue ratio-based method and frequency domain entropy-based method.In addition,the experimental results of the new untrained signal types show that our method can adapt to the detection of these new signals.Furthermore,the real-world signal detection experiment results show that the detection performance can be further improved by transfer learning.Finally,experiments under colored noise show that our proposed method has superior detection performance under colored noise,while the traditional methods have a significant performance degradation,which further validate the superiority of our method.     

基于信号集合势和连续性的认知无线电宽带频谱感知

针对传统感知算法依赖主用户信号与噪声先验信息,以及易受噪声功率估计不确定性影响的缺点,提出了一种基于信号集合势和连续性的宽带频谱感知方案。该方案将宽带频谱感知分为主用户占子带集合势的估计和子带位置判决两步。在两次不同感知结果中利用主用户连续占用子带的特性,有效地实现最终感知性能的提升。理论分析和仿真结果表明,该方案不仅能够解决传统感知方法依赖噪声和主用户信号先验信息的问题,而且对抗噪声功率不确定性具有鲁棒性。特别地,与传统的能量检测频谱感知算法相比,该算法能有效地实现宽带频谱盲感知。     

Optimal restoration of multichannel images based on constrained mean-square estimation

In this paper, we present an efficient algorithm for the problem of multichannel image restoration. Existing multichannel techniques do not provide sufficient flexibility for the simultaneous suppression of the noise process and the preservation of sharp detailed structure in the estimate. The approach introduced overcomes this inefficiency by introducing the prototype Wiener structure in the smoothing process of the estimate. The corresponding algorithm is obtained from the optimization of theconstrained mean-square-error (CMSE) criterion, which is interpreted as a structured regularized criterion. The CMSE estimate always has a meaningful structure and lies between the minimum mean-square error estimate and the pseudo-inverse solution. In addition, the CMSE approach enables the suppression of streak artifacts, which are often experienced due to the amplification of the noise process. In particular, the paper focuses on the selection of the regularization parameter, which can significantly affect the quality of the regularized estimate. Two selection techniques are introduced. The first technique develops the equivalence between the minimization of the weighted least-squares function and the solution of a set of nonlinear equations in the case of unstructured space-varying and nonstationary problem formulations. The second selection method is based on the Cramer-Rao bound on the expected variation of the stabilizing term. The CMSE approach is demonstrated through a multichannel restoration example and is compared to other restoration techniques.     

DOA估计算法评价准则在不同功率入射信号下的修正

针对复杂电磁环境中信号功率对入射信号波达方向（DOA）估计的影响问题进行研究,发现用于DOA估计算法性能分析的经典评价准则对不同功率入射信号存在局限性。针对该问题,首先证明了强信号功率会影响弱信号DOA估计性能,得到强信号功率增加会导致弱信号功率克拉美罗界上升,即弱信号DOA估计的均方根误差增加。然后分析了DOA估计算法的经典评价准则对分辨不同功率入射信号存在的局限性,通过蒙特卡洛实验验证了经典评价准则对分辨不同功率入射信号存在较大误判率,当弱信号信噪比低于5dB时,其误判率大于50%。最后本文提出了DOA估计算法新的评价准则,并仿真证明了新准则较经典准则更适用于分辨弱信号信噪比较低时的不同功率入射信号。所提出的评价准则可为基于空间谱估计的DOA估计算法性能分析提供参考依据。