Convergence analysis of blind image deconvolution via dispersion minimization

A new non‐linear adaptive filter called blind image deconvolution via dispersion minimization has recently been proposed for restoring noisy blurred images blindly. This is essentially a two‐dimensional version of the constant modulus algorithm that is well known in the field of blind equalization. The two‐dimensional extension has been shown capable of reconstructing noisy blurred images using partial a priori information about the true image and the point spread function in a variety of situations by means of simulations. This paper analyses the behaviour of the algorithm by investigating the static properties of the cost function and the dynamic convergence of the parameter estimates. The theoretical results are supported with computer simulations. Copyright © 2006 John Wiley & Sons, Ltd.     

Design of a near‐optimal adaptive filter in digital signal processor for active noise control

Adaptive filter has been applied in adaptive feedback and feedforward control systems, where the filter dimension is often determined by trial‐and‐error. The controller design based on a near‐optimal adaptive filter in digital signal processor (DSP) is developed in this paper for real‐time applications. The design integrates the adaptive filter and the experimental design such that their advantages in stability and robustness can be combined. The near‐optimal set of controller parameters, including the sampling rate, the dimension of system identification model, the dimension (order) of adaptive controller in the form of an FIR filter, and the convergence rate of adaptation is shown to achieve the best possible system performance. In addition, the sensitivity of each design parameter can be determined by analysis of means and analysis of variance. Effectiveness of the adaptive controller on a DSP is validated by an active noise control experiment. Copyright © 2007 John Wiley & Sons, Ltd.     

超声波换能器在次声波合成过程中失真补偿算法的研究

本文介绍了一种次声波的合成原理,并对次声波的发射装置进行了研究,主要分析了超声波换能器输出波形对次声波频率精度的影响.采用基于换能器解卷积的方法对回波信号进行处理,应用FIR数字滤波器及LMS自适应算法,来构造解卷积滤波器.经MATLAB 6.5计算机仿真实验结果证明,采用该方法对换能器进行解卷积后,得到的回波信号的带宽明显变宽,提高了次声波信号合成精度,进而改善了次声波的频谱精度.     

自适应滤波在系统辩识中的应用及MATLAB仿真

自适应FIR滤波器使用中要考虑的重要问题是优化调整滤波器参数的准则 ,该准则不仅要对滤波器性能提供有意义的度量 ,而且必须导出可实现的算法。论述了一种自适应调整FIR滤波器系数的基本算法 (LMS)方法 ,提出了一种基于自适应滤波理论的系统辩识数学模型。自适应滤波器的结构是具有可调系数h(0 ) ,h(1) ,…h(N - 1)的直接型FIR滤波器、未知系统和FIR模型并联连接且用相同的输入序列激励。仿真结果表明了这种模型和方法的正确性和鲁棒性     

On orthogonal realizations for adaptive IIR filters

Convergence speed is one of the main concerns in adaptive IIR filters. Fast convergence can be closely related to adaptive filter realization. However, with the exception of the lattice realization that is based on the nice properties of Szëgo orthonormal polynomials, no other adaptive IIR filter realization using orthonormal characteristics seems to be extensively studied in the literature. Furthermore, many orthogonal realizations for adaptive FIR filters, that are particularly suitable for rational modelling, have been proposed in the past years. Since rational orthogonal basis functions are a powerful tool for efficient system representation they seem attractive for adaptive IIR filters. In this paper, we present some theoretical results related to the properties of a generalized orthonormal realization when used for mean‐square output error minimization in a system identification application. One result is related to the low computational complexity of the updating gradient algorithm when some properties of the orthonormal realization are used. An additional result establishes conditions for the stationary points of the proposed updating algorithm. In order to confirm the expected performance of the new realization, some simulations and comparisons with competing realizations in terms of computational complexity and convergence speed are presented. Copyright © 2000 John Wiley & Sons, Ltd.     

基于多级嵌套维纳滤波自适应对角加载STAP算法

针对小快拍情况下的空时自适应处理（STAP）算法滤波性能下降,提出了基于多级嵌套维纳滤波（MSNWF）的自适应对角加载算法。算法充分利用MSNWF给出的干扰和噪声特征值信息,在分析MSNWF后向迭代实现过程基础上,推导出能递推实现的等价的自适应对角加载算法。通过在后向迭代过程中自适应选择加载量,增加稍许运算量的同时,较大程度地提高了空时自适应处理算法的滤波性能。仿真结果验证了算法的有效性。     

Analysis and performance of CMA blind deconvolution for image restoration

In this paper we study the applicability of classical blind deconvolution methods such as constant modulus algorithm (CMA) for blind adaptive image restoration. The requirements such as the source to be white, uniformly distributed and zero mean, which yield satisfactory convergence in the data communication application context, are revisited in the image restoration context, where a linear deblur kernel needs to be blindly adapted to compensate for an unknown image blur kernel with the objective to recover a source ground truth image. Through analysis and performance studies, we show that the performance of CMA is adversely affected by the intrinsic spatial correlation of natural images and by any deviation of their distribution from being platykurtic. We also show that decorrelation techniques designed to overcome spatial correlation cannot be effectively applied to rectify CMA performance for blind adaptive image restoration. Copyright © 2014 John Wiley & Sons, Ltd.     

结构稀疏通道先验盲图像去模糊方法

针对盲图像去模糊过程中主结构不准确和边缘不清晰问题,提出了一种结构稀疏通道先验(SSCP)盲图像去模糊方法。SSCP表示模糊图像比清晰图像具有更少结构稀疏通道的先验方法。利用SSCP的性能特性,将其作为新的正则化项引入经典去模糊模型,构建盲去模糊新模型,实现对模糊核的准确估计。通过坐标下降法,交替优化求解潜像与模糊核变量。最后,通过反卷积得到去模糊的清晰复原图像,在基准数据集和自然状态模糊图像上开展主观和客观对比实验,并进行人脸和低亮度真实模糊图像的应用拓展实验。实验结果表明,提出的方法在模糊去除、结构恢复、边缘保留和视觉效果方面的性能比经典去模糊方法平均提高了1.72%,通过该方法设计出的计算装置能够实现机器视觉领域中模糊图像的高精度清晰化处理。     

Blind deconvolution by a Newton method on the non‐unitary hypersphere

Blind deconvolution is an inverse filtering technique that has received increasing attention from academia as well as industry because of its theoretical implications and practical applications, such as in speech dereverberation, nondestructive testing and seismic exploration. An effective blind deconvolution technique is known as ‘Bussgang’, which relies on the iterative Bayesian estimation of the source sequence. Automatic gain control in blind deconvolution keeps constant the energy of the inverse filter impulse response and controls the magnitude of the estimated source sequence. The aim of the present paper is to introduce a class of Newton‐type algorithms to optimize the Bussgang cost function on the inverse‐filter parameter space whose geometrical structure is induced by the automatic‐gain‐control constraint. As the parameter space is a differentiable manifold, the Newton‐like optimization method is formulated in terms of differential geometrical concepts. The present paper also discusses convergence issues related to the introduced Newton‐type optimization algorithms and illustrates their performance on a comparative basis.Copyright © 2012 John Wiley & Sons, Ltd.     

医学超声病灶图像预处理

图像滤波技术在图像处理中占有重要的地位。其中医学病灶超声图像主要被斑点噪声污染,对医生诊断病情带来干扰。针对医学超声图像噪声的特点提出了自适应中值滤波器,并与经典中值滤波器对含有不同噪声密度的胆囊超声图像进行去噪处理,对实验结果对比分析。结论表明:自适应中值滤波较经典中值滤波在对噪声密度较大的图像进行去噪时,能较好的保持图像细节信息,它能够有效改善图像质量。自适应中值滤波器较其他非线性滤波器有更好的视觉效果。     

A novel approach to introducing adaptive filters based on the LMS algorithm and its variants

This paper presents a new approach to introducing adaptive filters based on the least-mean-square (LMS) algorithm and its variants in an undergraduate course on digital signal processing. Unlike other filters currently taught to undergraduate students, these filters are nonlinear and time variant. This proposal introduces adaptive filtering in the context of a linear time-invariant system using a real problem. In this way, introducing adaptive filters using concepts already familiar to the students motivates their interest through practical application. The key point for this simplification is that the input to the filter is constant so that the adaptive filter becomes linear. Therefore, a complete arsenal of mathematical tools, already known by the students, is available to analyze the performance of the filters and obtain the key parameters to adaptive filters, e.g., speed of convergence and stability. Several variants of the basic LMS algorithm are described the same way.     

自适应滤波器的FPGA实现

本文采用自上而下的设计思想,用FPGA实现了自适应滤波器.自适应滤波器选择FIR滤波器结构,采用了改进的LMS算法,从而使得在同样的硬件资源下滤波的速度可提高一倍;本论文用VHDL编写代码,用MaxplusII进行编译、综合和仿真,FPGA器件选用ALTERA公司的FLEX10K系列3万门的芯片,综合结果显示,所设计的自适应滤波器使用FLEX10K30的70%的资源;对综合后的网表进行了仿真,当时钟周期取40ns时,滤波器仍能够很好地消除噪声.     

基于改进的各向异性模型对IVUS图像降噪算法

针对血管内超声图像中的强背景噪声和边缘模糊等问题,提出了一种改进的各项异性扩散滤波算法.引入中值滤波,将滤波后的梯度模代替传统各向异性滤波中原始图像的梯度模,以控制扩散的过程,并能较好地保持边缘的特性;将各向异性扩散方程的常规扩散方向由4个方向扩展为8个方向,可保留更多的图像细节;并提出了一种自适应选取扩散门限的方法,解决了滤波和边缘保持的矛盾.实验结果表明,改进的算法在滤除噪声和保留边缘方面有着比较满意的效果,为以后血管内超声图像中外膜的提取提供了基础.     

The Kalman filter in the context of adaptive filter theory

Model‐based adaptive algorithms are usually derived with the help of the Wiener‐Hopf equation based on empirical statistics. They are often interpreted as an extension to their model‐independent counterparts, i.e. the stochastic‐gradient based adaptive filters. As a consequence, it is generally not considered worthwhile to show the analogy between Kalman filters and adaptive filters. This article pursues just these two goals. First, it tries to remove the notion that the Kalman filter is a complicated and unnecessary detour from the subject of adaptive filtering. Second, the advantage of a deeper insight into adaptive algorithms from Kalman's viewpoint emerges from our treatment. Based on a time‐varying FIR filter model, the Kalman filter is completely derived and serves as a general framework for the special case of model‐based adaptive filters. Copyright © 2004 John Wiley & Sons, Ltd.     

基于指数同态滤波耦合细节锐化规则的 红外图像增强算法

为了解决当前红外图像增强方法存在的光晕及细节模糊等不足,提出了指数同态滤波耦合细节锐化规则的红外图像增强算法.基于同态滤波方法,通过频域中的像素点与中心像素点的距离,构造指数型同态函数,以同时完成图像的去噪和增强对比度处理.联合相位一致性方法和自适应高提升滤波方法,构造了细节锐化机制.在图像的细节锐化中,利用相位一致性方法,通过傅里叶变换,准确提取出图像的细节特征.并引入高提升滤波方法,利用图像的均值,构造自适应的锐化因子,以形成自适应高提升滤波方法,对提取的图像细节特征进行锐化,完成图像细节内容的增强.实验结果表明,较当前的红外图像增强算法而言,所提算法具有更好的增强效果,其增强图像呈现出更为理想的对比度和更为清晰的图像边缘.     

A unifying framework for the analysis of proportionate NLMS algorithms

Despite being a de facto standard in sparse adaptive filtering, the two most important members of the class of proportionate normalised least mean square (PNLMS) algorithms are introduced empirically. Our aim is to provide a unifying framework for the derivation of PNLMS algorithms and their variants with an adaptive step‐size. These include algorithms with gradient adaptive learning rates and algorithms with adaptive regularisation parameters. Convergence analysis is provided for the proportionate least mean square (PLMS) algorithm in both the mean and mean square sense and bounds on its parameters are derived. An alternative, more insightful approach to the convergence analysis is also presented and is shown to provide an estimate of the optimal step‐size of the PLMS. Incorporating the so obtained step‐size into the PLMS gives the standard PNLMS together with a unified framework for introducing other adaptive learning rates. Simulations on benchmark sparse impulse responses support the approach. Copyright © 2014 John Wiley & Sons, Ltd.     

一种FIR高阶多通带数字滤波器的优化设计方法

为有效提高有限冲激响应FIR(FiniteImpulseResponse)高阶数字滤波器优化设计速度和精度,根据FIR线性相位滤波器的幅频特性,提出了一种基于激励矩阵为Hd-CTW的神经网络算法。该算法的主要思想是用神经网络算法优化设计的FIR滤波器的幅频特性与理想滤波器的幅频特性在整个通带和阻带范围内的误差平方和为最小,算法不涉及逆矩阵运算。为了保证该算法的收敛性,提出并证明了神经网络算法的收敛性定理,为神经网络学习率的选择提供了理论依据。该算法的主要特点是可实现样本集数据的并行训练,有效提高了计算速度。为了验证该算法的有效性,给出了多通带FIR高阶数字滤波器优化设计实例,仿真结果表明了该算法具有高的计算精度和快的计算速度。     

Self‐tuning fusion Kalman filter weighted by scalars and its convergence analysis for multi‐channel autoregressive moving average signals

For the multi‐sensor multi‐channel autoregressive (AR) moving average signals with white measurement noises and an AR‐colored measurement noise, a multi‐stage information fusion identification method is presented when model parameters and noise variances are partially unknown. The local estimators of model parameters and noise variances are obtained by the multidimensional recursive instrumental variable algorithm and correlation method, and the fused estimators are obtained by taking the average of the local estimators. They have the strong consistency. Substituting them into the optimal information fusion Kalman filter weighted by scalars, a self‐tuning fusion Kalman filter for multi‐channel AR moving average signals is presented. Applying the dynamic error system analysis method, it is proved that the proposed self‐tuning fusion Kalman filter converges to the optimal fusion Kalman filter in a realization, so that it has asymptotic optimality. A simulation example for a target tracking system with three sensors shows its effectiveness. Copyright © 2014 John Wiley & Sons, Ltd.     

横向时延滤波和IQ正交滤波的滤波效果仿真

由于横向时延滤波和IQ正交滤波在稳定性、收敛速度和误差率等方面的性能差异对于最小均方算法(LMS,Least Mean Squares)在工程上的实际应用具有参考意义,采用数值仿真的方法模拟了两者实现自适应最小均方算法的具体过程,并对比分析了它们的滤波性能。仿真结果显示IQ正交滤波具有更高的稳定性、更快的收敛速度、更小的误差率,其滤波性能优于横向时延滤波。IQ正交滤波器的阶数为2阶,而横向时延滤波器的阶数通常>10,滤波器阶数越多引入的权噪声也会相对增加,对于稳定性、收敛速度和误差率都是不利的,因此实际应用中优先选择阶数较少的IQ正交滤波器。     

Adaptive filtering‐based multi‐innovation gradient algorithm for input nonlinear systems with autoregressive noise

In this paper, by means of the adaptive filtering technique and the multi‐innovation identification theory, an adaptive filtering‐based multi‐innovation stochastic gradient identification algorithm is derived for Hammerstein nonlinear systems with colored noise. The new adaptive filtering configuration consists of a noise whitening filter and a parameter estimator. The simulation results show that the proposed algorithm has higher parameter estimation accuracies and faster convergence rates than the multi‐innovation stochastic gradient algorithm for the same innovation length. As the innovation length increases, the filtering‐based multi‐innovation stochastic gradient algorithm gives smaller parameter estimation errors than the recursive least squares algorithm.