Blind source extraction from convolutive mixtures in ill-conditioned multi-input multi-output channels

This paper presents a new approach to blind source extraction from convolutive mixtures in multi-input multi-output (MIMO) channels. Two ill-conditioned cases are considered: the number of sensors is less than the number of sources and the number of sensors is greater than or equal to the number of sources but the system is noninvertible. Although there exist several works related to ill-conditioned dynamic MIMO channels, especially on blind channel identification, how to obtain a true source only from observable convolutive mixtures is still an open problem. In this paper, beginning with introducing two blind extraction models for blind deconvolution in ill-conditioned MIMO channels, we discuss the extractability issue. Results from our extractability analysis (a necessary and sufficient condition) show that it is possible to extract individual sources from the outputs. Furthermore, all potentially separable sources (at most equal to the number of sensors) can be extracted sequentially based on these extraction models. A cost function based on cross cumulant is discussed along with the Gauss-Newton algorithm. Finally, a simulation example is presented for illustration.     

基于卡尔曼滤波的同步盲系统辨识与解卷积方法

在盲信道均衡或盲语音去混响应用中,盲多信道系统辨识通常是信号解卷积的前提条件,即盲辨识过程后跟一个解卷积过程。本文提出一种基于卡尔曼滤波的同步盲系统辨识与解卷积方法,其中卡尔曼滤波的状态矢量由多信道系统参数与源信号矢量组成,过程方程和测量方程则建立在单输入-多输出系统(SIMO)的输入输出关系及信道间交叉关联关系(Cross Relation)基础上。此外,盲系统辨识部分与解卷积部分是可以解耦的,生成两个看似独立的卡尔曼滤波问题,并且这两个卡尔曼滤波问题可以实现并行计算。与级联结构相比,这种并行结构更有利于算法优化和实时信号处理。仿真表明,对于无噪声理想信号模型,本算法可以实现完全系统辨识和解卷积(信号误差比可达到100 dB以上),说明理论正确;对于实测的混响语音信号亦可以实现一定的去混响效果。      

Blind deconvolution of spotted image based on slice selection of third-order moment

The 1D blind deconvolution algorithm using maximum time delay slice of the third-order moment ((MTDS-TOM) [Lu, W]) is extended to 2D blind deconvolution for spotted image deblurring. A scaled and shifted version of the image is obtained using a special slice selected from its third-order moment, which is estimated using a 4D blind deconvolution. An application of the proposed method for removing the optical blur of a microarray image is given.     

Iterative multichannel blind deconvolution method for temporally colored sources

An iterative separation approach, i.e. source signals are extracted and removed one by one, is proposed for multichannel blind deconvolution of colored signals. Each source signal is extracted in two stages: a filtered version of the source signal is first obtained by solving the generalized eigenvalue problem, which is then followed by a single channel blind deconvolution based on ensemble learning. Simulation demonstrates the capability of the approach to perform efficient mutichannel blind deconvolution.     

A two-stage algorithm for MIMO blind deconvolution of nonstationarycolored signals

A new two-stage algorithm is proposed for the deconvolution of multi-input multi-output (MIMO) systems with colored input signals. While many blind deconvolution algorithms in the literature utilize high order statistics of the output signal for white input signals, the additional information contained in colored input signals allows the design of second-order statistical algorithms. In fact, practical signal sources such as speech signals do have distinct, nonstationary, colored power spectral densities. We present a two-stage signal separation approach in which the first step utilizes a matrix pencil between output auto-correlation matrices at different delays, whereas the second stage adopts a subspace method to identify and deconvolve MIMO systems     

Multiple frame projection based blind deconvolution

Important a priori information available for blind deconvolution in problems such as astronomical imaging and remote sensing is the information in the multiple frame images in which the object is common for each frame but the point spread function varies. A projection based blind deconvolution algorithm for solving the multiple frame case is proposed     

Relative optimization for blind deconvolution

We propose a relative optimization framework for quasi-maximum likelihood (QML) blind deconvolution and the relative Newton method as its particular instance. Special Hessian structure allows fast Newton system construction and solution, resulting in a fast-convergent algorithm with iteration complexity comparable to that of gradient methods. We also propose the use of rational infinite impulse response (IIR) restoration kernels, which constitute a richer family of filters than the traditionally used finite impulse response (FIR) kernels. We discuss different choices of nonlinear functions that are suitable for deconvolution of super- and sub-Gaussian sources and formulate the conditions under which the QML estimation is stable. Simulation results demonstrate the efficiency of the proposed methods.     

Blind deconvolution using a variational approach to parameter, image, and blur estimation.

Following the hierarchical Bayesian framework for blind deconvolution problems, in this paper, we propose the use of simultaneous autoregressions as prior distributions for both the image and blur, and gamma distributions for the unknown parameters (hyperparameters) of the priors and the image formation noise. We show how the gamma distributions on the unknown hyperparameters can be used to prevent the proposed blind deconvolution method from converging to undesirable image and blur estimates and also how these distributions can be inferred in realistic situations. We apply variational methods to approximate the posterior probability of the unknown image, blur, and hyperparameters and propose two different approximations of the posterior distribution. One of these approximations coincides with a classical blind deconvolution method. The proposed algorithms are tested experimentally and compared with existing blind deconvolution methods.     

Underwater image restoration by means of blind deconvolution approach

Although the use of blind deconvolution of image restoration is a widely known concept, little literatures have discussed in detail its application in the problem of restoration of underwater range-gated laser images. With the knowledge of the point spread function (PSF) and modulation transfer function (MTF) of water,underwater images can be better restored or enhanced. We first review image degradation process and Wells' small angle approximation theory, and then provide an image enhancement method for our underwater laser imaging system by blind deconvolution method based on small angle approximation. We also introduce a modified normalized mean square error (NMSE) method to validate the convergence of the blind deconvolution algorithm which is applied in our approach. The results of different initial guess of blind deconvolution are compared and discussed. Moreover, restoration results are obtained and discussed by intentionally changing the MTF parameters and using non-model-based PSF as the initial guess.     

基于非参数密度估计的多通道盲解卷积

非参数密度估计方法被用来直接估计在自然梯度盲解郑积算法中遇到的评价函数(score function)。与用一个非线性函数简单地代替评价函数相比较,这种直接估计评价函数的方法的主要优点是:它可以用来对杂系混合信号,即同时包含超高斯和亚高斯的信号,进行盲解卷积。因为评价函数可以被直接的估计出来,因此,就不需要针对不同的源信号选择不同的非线性函数来代替评价函数。这种方法可以用在更加“盲”的情况。     

On the use of Lyapunov criteria to analyze the convergence of blinddeconvolution algorithms

We present an approach to determine sufficient conditions for the global convergence of iterative blind deconvolution algorithms using finite impulse response (FIR) deconvolution filters. The novel technique, which incorporates Lyapunov's direct method, is general, flexible, and can be easily adapted to analyze the behavior of many types of nonlinear iterative signal processing algorithms. Specifically, we find sufficient conditions to guarantee a unique solution for the NAS-RIF algorithm used for blind image restoration. We determine that in many cases, there exists a tradeoff between the quality of the deconvolution result and the uniqueness of the solution. A procedure to determine the length of the deconvolution filter to guarantee a unique solution is established     

一种新的盲解卷积准则和算法

定义了盲解卷积问题的期望解后 ,将二阶累积量和四阶累积量合并为一个新的统计量 ,称为归一化累积量 ,考察信号通过线性时不变系统时归一化累积量的特性 ,形成一个基于归一化累积量的盲解卷积准则 ;借助于经典的最陡梯度算法 ,导出了一种新的盲均衡算法 ,计算机模拟验证了该算法     

基于点扩散函数支持域扩展的多帧未匹配退化图像盲解卷积复原

多帧盲解卷积算法利用多帧退化图像进行复原可以获得清晰原始图像和点扩散函数的信息,受到了很多研究者的关注。目前大部分多帧盲解卷积算法都需要对多帧退化图像进行匹配预处理,以消除图像间平移引入的算法求解误差。本文利用频率内的多帧盲解卷积算法对未匹配的退化图像进行处理,不需要进行预匹配处理,只需要对点扩散函数的支持域进行扩展就可以复原获取清晰化的图像。利用傅里叶变换的性质对该方法的可行性进行了说明。同时对该方法进行了数字仿真实验,复原结果中的点扩散函数发生了相对移动消除了图像间未匹配的影响,证实了本文方法的有效性。     

面向多路源信号的单通道盲去卷积算法研究

传统的单通道盲去卷积的方法存在仅能从混合信号中分离出2路源信号的局限,考虑到以上问题,该文提出一种基于优化的深度卷积生成对抗网络的单通道盲去卷积算法(SCBDC),能从1路混合信号中分离和解卷积出3路以上的独立源信号和混合矩阵。该文实验在汉字和遮挡图像数据集上进行,随机选择4路信号与混合矩阵进行卷积混合,实验结合峰值信噪比(PSNR)和信号相关性指标来评价分离的效果,结果显示,该算法能够有效地分离出多路源信号并去卷积。     

Gradient Adaptive Algorithms for Contrast-Based Blind Deconvolution

This paper presents extensions of stochastic gradient independent component analysis (ICA) methods to the blind deconvolution task. Of particular importance in these extensions are the constraints placed on the deconvolution system transfer function. While unit-norm constrained ICA approaches can be directly applied to the prewhitened blind deconvolution task, an allpass filter constraint within the optimization procedure is more appropriate. We show how such constraints can be approximately imposed within gradient adaptive finite-impulse-response (FIR) filter implementations by proper extensions of gradient techniques within the Stiefel manifold of orthonormal matrices. Both on-line time-domain and block-based frequency-domain algorithms are described. Simulations verify the superior performance behaviors provided by our allpass-constrained algorithms over standard unit-norm-constrained ICA algorithms in blind deconvolution tasks.     

盲源分离和盲反卷积

盲信号处理是信号处理领域的热点研究问题,盲源分离和盲反卷积是盲信号处理的重要组成部分近年来取得许多重要进展.本文主要介绍盲源分离和盲反卷积的基本模型、数学原理和研究进展;分析了各种方法的特点并指出了进一步的研究方向.     

Multidimensional system identification through blind deconvolution

By invoking characteristics of the recently introduced zero-sheet of the spectrum of a signal having finite (or compact) support, it is noted that the multidimensional system identification problem should be solvable through blind deconvolution, that is, the system response function should be inferrable in the absence of prior knowledge of the signal which excites the system. It is pointed out that practical blind deconvolution can only be effected iteratively at present. An iterative blind identification algorithm is described and is illustrated by recovery of images from blurred versions contaminated with noise of varying levels. Successful blind deconvolution is achieved without invoking prior knowledge of either the forms or the supports of either the original images or the point spread functions, which respectively correspond to exciting signals and response functions.     

基于盲反卷积的盲自适应滤波器设计

通过盲反卷积的算法来实现盲自适应滤波,阐述了盲反卷积滤波器的工作原理及基本结构模型,通过调整滤波器系数来实现滤波,以便更好地跟踪信号的变化,最终实现自适应滤波,并借用Matlab仿真平台设计出自适应滤波器,验证了它的设计性能。     

AN IMPROVED FAST BLIND DECONVOLUTION ALGORITHM BASED ON DECORRELATION AND BLOCK MATRIX

In order to alleviate the shortcomings of most blind deconvolution algorithms,this paper proposes an improved fast algorithm for blind deconvolution based on decorrelation technique and broadband block matrix. Althougth the original algorithm can overcome the shortcomings of current blind deconvolution algorithms,it has a constraint that the number of the source signals must be less than that of the channels. The improved algorithm deletes this constraint by using decorrelation technique. Besides,the improved algorithm raises the separation speed in terms of improving the computing methods of the output signal matrix. Simulation results demonstrate the validation and fast separation of the improved algorithm.