A probabilistic approach to multivariable robust filtering andopen-loop control

A new approach to robust filtering, prediction, and smoothing of discrete-time signal vectors is presented. Linear time-invariant filters are designed to be insensitive to spectral uncertainty in signal models. The goal is to obtain a simple design method, leading to filters which are not overly conservative. Modeling errors are described by sets of models, parameterized by random variables with known covariances. These covariances could either be estimated from data or be used as robustness “tuning knobs.” A robust design is obtained by minimizing the ℋ₂-norm or, equivalently, the mean square estimation error, averaged with respect to the assumed model errors. A polynomial solution, based on an averaged spectral factorization and a unilateral Diophantine equation, is derived. The robust estimator is referred to as a cautious Wiener filter. It turns out to be only slightly more complicated to design than an ordinary Wiener filter. The methodology can be applied to any open-loop filtering or control problem. In particular, we illustrate this for the design of robust multivariable feedforward regulators, decoupling and model matching filters     

含噪语音实时迭代维纳滤波

针对传统去噪方法在强背景噪声情况下,提取声音信号的能力变弱甚至失效与对不同噪声环境适应性差,提出了迭代维纳滤波声音信号特征提取方法。给出了语音噪声频谱与功率谱信噪比迭代更新机制与具体实施方案。实验仿真表明,该算法能有效地去噪滤波,显著地提高语音识别系统性能,且在不同的噪声环境和信噪比条件下具有鲁棒性。该算法计算代价小,简单易实现,适用于嵌入式语音识别系统。     

Robust Wiener filtering with non-parametric spectral uncertainty

In this article, robust least-squares filtering problems are considered for non-parametric multivariate spectral uncertainty defined by the so-called spectral band and generalised-moment constraints. Its major aim is to provide a basis for computing approximate solutions to worst-case, Wiener-filtering optimisation problems involving causal filters and multivariate signals. It hinges upon associating upper and lower bounds on the minimum worst-case performance achievable with causal filters with linear-cost/linear matrix inequality (LC/LMI)-constraint optimisation problems. On the basis of a Lagrangean duality formulation for the worst-case, least-squares performance of a given filter, upper bounds on it are obtained as the optimal values of LC/LMI problems. Then, for linearly parameterised classes of filter transfer functions, a causal filter which optimises such an upper bound on worst-case performance can also be obtained from an LC/LMI optimisation problem. To estimate the amount of conservatism incurred when relying on such upper bounds, optimal, nominal, least-squares performance for a given pair of power spectral densities (for the information and noise signal) is maximised over finite-dimensional, linearly parameterised classes of the latter. Again, such problems are shown to be equivalent to LC/LMI problems and the corresponding optimal values are lower bounds on the minimum worst-case, least-squares error achievable in the original robust filtering problem (say, μ_*). Finally, two simple numerical examples are presented to illustrate how causal filters can be obtained whose worst-case, least-squares performance is quite close to the optimal one (i.e. μ_*).     

噪声环境下的鲁棒性说话人识别

在实际应用中,噪声或信道干扰导致说话人识别(SR)识别性能急剧下降。针对该问题,本文分析传统方法的优缺点并提出相应的系统解决方案:采用维纳滤波对语音信号进行前端处理;以MFCC声道特征结合基频(F0)韵律特征来提高识别系统的鲁棒性。实验结果表明:维纳滤波能有效地消除噪声影响;经维纳滤波处理后,使得F0-MFCC联合模型能更好的区分说话人。可以看出在噪声环境下系统的综合性能得到很大改善。     

Time-Limited Time-Invariant Wiener Filtering

For the estimation of a signal observed with additive white noise, it is shown that the optimum linear least-squares filter constrained to have its impulse response time-limited to the interval [0,T] satisfies a truncated version of the Wiener-Hopf equation. To solve this equation the covariance for the observed process need only be known for time lags less than T. There is a unique extension of the covariance for lags greater than T, for which the time-limited filter is the optimum Wiener filter; furthermore this same extension is that extension of the covariance for which the optimum Wiener filter gives maximum mean square error, i.e., given limited covariance information we have found the “worst possible” extension of the known information. Parallels are drawn with discrete-time maximum-entropy spectral analysis.     

基于维纳滤波的超声增强实现方法

超声在传播时,由于受到材质不均匀、材料内部杂质等的影响而使接收信号受到噪声的干扰,这种干扰有时会淹没所检测的裂纹信号,因此必须要经过增强处理。声学增强处理常用的方法是维纳滤波。本文提出维纳滤波用于超声增强的具体实现方法,即首先统计平均无脉冲段的初始噪声功率谱,然后自适应计算带干扰超声段功率谱,最后进行维纳滤波。超声数据在不同信噪比下的维纳滤波实验表明了所提方法的有效性,超声维纳去噪方法与谱减法一样能够降低超声回波中的噪声,且更加有效。     

Noise reduction in biomedical speech signal processing based on time and frequency Kalman filtering combined with spectral subtraction

The goal of this paper is to study and propose a new technique for noise reduction used during the reconstruction of speech signals, particularly for biomedical applications. The proposed method is based on Kalman filtering in the time domain combined with spectral subtraction. Comparison with discrete Kalman filter in the frequency domain shows better performance of the proposed technique. The performance is evaluated by using the segmental signal-to-noise ratio and the Itakura-Saito’s distance. Results have shown that Kalman’s filter in time combined with spectral subtraction is more robust and efficient, improving the Itakura-Saito’s distance by up to four times.     

Robust ℋ2 filtering for LTI systems with linear fractional representation

This article introduces a new approach to ?₂ robust filtering design for continuous and discrete-time LTI systems subjected to linear fractional parameter uncertainty representation. The novelty consists on the determination of a performance certificate in terms of the gap between lower and upper bounds of a minimax programming problem which defines the optimal robust filter and the associated equilibrium cost. The calculations are performed through convex programming methods, applying slack variables, known as multipliers, to handle the fractional dependence of the plant transfer function with respect to the parameter uncertainty. The theory is illustrated by means of an example borrowed from the literature and a practical application involving the design of a robust filter for the load voltage estimation on a transmission line with a stub feeding an unknown resistive load.     

一种鲁棒性的基于运动估计的自适应时空域视频去噪算法

提出了一种鲁棒的基于运动估计的自适应时空域视频去噪算法。在运动估计前的自适应维纳滤波,提高了运动估计的准确性与匹配率;在运动估计后基于小块的再次判断以及Duncan滤波器的采用,提高了运动估计的鲁棒性。实验数据表明,此算法取得了很好的预期效果。     

Minimax linear smoothing for capacities: The case of correlated signals and noise

Results of an earlier paper giving minimax linear smoothers for the problem of estimating a homogeneous signal field in an additive orthogonal noise field when both have uncertain spectral properties, are extended to the case in which the signal and noise fields are arbitrarily correlated. As before, spectral uncertainty is modeled by assuming that the spectral measures of the signal and noise fields lie in classes of measures generated by two-alternating Choquet capacities. It is demonstrated that this problem admits a general solution in terms of the Huber-Strassen derivative between the capacities that generate the uncertainty sets, and that the least favorable spectra for smoothing in orthogonal noise are also the least favorable marginal spectra for smoothing in correlated noise. The resulting filter is seen to be a zonal filter that also arises as the solution to an analogous problem in (nonparametric) minimax hypothesis testing. These new results extend the applicability of minimax robust smoothing techniques to application involving signal-dependent noise phenomena, such as multipath and clutter, which are usually difficult to model precisely.     

引入修正因子的局部维纳滤波图像去噪

维纳滤波是一种古典的去噪方法,它是最小均方误差意义上的最优线性滤波。在对它的性能分析后,噪声方差修正因子被引入。实验结果表明,这一方法虽然简单,但是有效改善了传统局部维纳滤波的性能。     

Transforming Binary Uncertainties for Robust Speech Recognition

Recently, several algorithms have been proposed to enhance noisy speech by estimating a binary mask that can be used to select those time-frequency regions of a noisy speech signal that contain more speech energy than noise energy. This binary mask encodes the uncertainty associated with enhanced speech in the linear spectral domain. The use of the cepstral transformation smears the information from the noise dominant time-frequency regions across all the cepstral features. We propose a supervised approach using regression trees to learn the nonlinear transformation of the uncertainty from the linear spectral domain to the cepstral domain. This uncertainty is used by a decoder that exploits the variance associated with the enhanced cepstral features to improve robust speech recognition. Systematic evaluations on a subset of the Aurora4 task using the estimated uncertainty show substantial improvement over the baseline performance across various noise conditions.     

用于自动语音识别系统的切换语音功率谱估计算法

针对语音识别系统在噪声环境下不能保持很好鲁棒性的问题,提出了一种切换语音功率谱估计算法。该算法假设语音的幅度谱服从Chi分布,提出了一种改进的基于最小均方误差（MMSE）的语音功率谱估计算法。然后,结合语音存在的概率（SPP）,推导出改进的基于语音存在概率的MMSE估计器。接下来,将改进的MSME估计器与传统的维纳滤波器结合。在噪声干扰比较大时,使用改进的MMSE估计器来估计纯净语音的功率谱,当噪声干扰较小时,改用传统的维纳滤波器以减少计算量,最终得到用于识别系统的切换语音功率谱估计算法。实验结果表明,所提算法相比传统的瑞利分布下的MMSE估计器在各种噪声的情况下识别率平均提高在8个百分点左右,在去除噪声干扰、提高识别系统鲁棒性的同时,减小了语音识别系统的功耗。     

Two empirical methods for improving the performance of statistical multirate high-resolution signal reconstruction

The problem of reconstructing a known high-resolution signal from a set of its low-resolution parts exposed to additive white Gaussian noise is addressed in this paper from the perspective of statistical multirate signal processing. To enhance the performance of the existing high-resolution signal reconstruction procedure that is based on using a set of linear periodically time-varying (LPTV) Wiener filter structures, we propose two empirical methods combining empirical mode decomposition- and least squares support vector machine regression-based noise reduction schemes with these filter structures. The methods originate from the idea of reducing the effects of white Gaussian noise present in the low-resolution observations before applying them directly to the LPTV Wiener filters. Performances of the proposed methods are evaluated over one-dimensional simulated signals and two-dimensional images. Simulation results show that, under certain conditions, considerable improvements have been achieved by the proposed methods when compared with the previous study that only uses a set of LPTV Wiener filter structures for the signal reconstruction process.     

An RBFN–Wiener hybrid filter using higher order signal statistics

In this paper we propose a radial basis function network (RBFN) based nonlinear filter with a basic framework of a linear Wiener filter. In addition, in order to improve the filtering performance, we further propose a novel nonlinear filter, which is synthesized by a hybridization of an RBFN filter and a linear Wiener filter. The proposed filters are realized with a least mean square error scheme using higher order statistics of a target signal and an observation noise.The validity and the effectiveness of the proposed filters have been verified by applying them to the actual filtering problems of the noisy images.     

Design and experimental evaluation of robust controllers for a two-wheeled robot

The paper presents the design and experimental evaluation of two alternative μ-controllers for robust vertical stabilisation of a two-wheeled self-balancing robot. The controllers design is based on models derived by identification from closed-loop experimental data. In the first design, a signal-based uncertainty representation obtained directly from the identification procedure is used, which leads to a controller of order 29. In the second design the signal uncertainty is approximated by an input multiplicative uncertainty, which leads to a controller of order 50, subsequently reduced to 30. The performance of the two μ-controllers is compared with the performance of a conventional linear quadratic controller with 17th-order Kalman filter. A proportional-integral controller of the rotational motion around the vertical axis is implemented as well. The control code is generated using Simulink® controller models and is embedded in a digital signal processor. Results from the simulation of the closed-loop system as well as experimental results obtained during the real-time implementation of the designed controllers are given. The theoretical investigation and experimental results confirm that the closed-loop system achieves robust performance in respect to the uncertainties related to the identified robot model.     

Choosing weight functions for filtering SAR

One of the biggest problems in automatic processing of synthetic aperture radar (SAR) imagery is the large amount of noise due to speckle. Some form of smoothing is needed before interpretation can take place. Traditionally, the amount of smoothing has been chosen in an arbitrary manner. Optimal smoothing filters, such as the Wiener filter, may be derived, but their implementation is a demanding task in most image handling systems. This paper suggests that by constraining image autocorrelations and smoothing filter weights to be functions with few parameters, a useful saving in the complexity of algorithms may be achieved, with little loss of filter performance. It is also shown that the performance of this approach is robust to the form of the autocorrelation function.     

Speech enhancement with an adaptive Wiener filter

This paper proposes an adaptive Wiener filtering method for speech enhancement. This method depends on the adaptation of the filter transfer function from sample to sample based on the speech signal statistics; the local mean and the local variance. It is implemented in the time domain rather than in the frequency domain to accommodate for the time-varying nature of the speech signals. The proposed method is compared to the traditional frequency-domain Wiener filtering, spectral subtraction and wavelet denoising methods using different speech quality metrics. The simulation results reveal the superiority of the proposed Wiener filtering method in the case of Additive White Gaussian Noise (AWGN) as well as colored noise.     

An adaptive coherence filter

This paper derives an adaptive coherence filter for canceling interference from a signal of interest whose power spectral density is symmetric. A basic property of the Fourier transform of real signals is that their spectra are Hermitian symmetric. This property is exploited to determine which part of a spectrum is interference and which part is the signal of interest. An unconstrained Wiener filter is derived that exploits the frequency domain symmetry of the signal of interest. While the adaptive coherence filter is based on the Fourier transform property of real signals, an extension of the algorithm is provided so the filter can be used on any signal that displays spectral symmetry. A practical method for implementing the filter is provided. The filter has application in the area of telecommunications, but is applicable in wireless communication applications where a signal, that displays spectral symmetry, is corrupted by interfering signals within the signal of interest's bandwidth.     

Wiener filter-based wavelet domain denoising

The wavelet domain Wiener filter has been widely adopted as an effective image denoising method that has low complexity. In this paper we propose a novel Wiener filter with high-resolution estimation that determines the signal power while preserving the edge information. We assume that a noisy image is composed of noise and the original image, which are mutually orthogonal. Based on this assumption, we utilize the local covariance to obtain high-resolution coefficients from the low-resolution coefficients and to estimate the signal variance in the Wiener filter by using the high resolution values. The experimental results show that the proposed algorithm improves the objective and subjective performance significantly.