基于零空间表示和最大似然的欠定盲源分离方法

针对欠定情况下源数的估计、解混叠矩阵和源信号恢复关键技术,提出一种源数未知的欠定盲源分离算法,首先利用S变换和聚类技术相结合来估算源数和混叠矩阵,然后将源信号以零空间形式表示,再通过最大似然估计关于其后验概率以达到恢复源信号的目的。仿真实验结果表明了该方法不仅能同时分离服从超高斯分布和亚高斯分布的源信号,且比其他传统的方法具有更优越的估计性能。     

动态变化混叠模型下盲源分离中的源数估计

在进行欠定盲分离时,特别是对于源信号数目及混合矩阵动态变化的情况,常规的欠定盲分离及源数估计方法不能对源信号数目的变化时刻做出判断,因此很难实现动态变化的源信号数目实时和准确的估计。针对这个问题,提出了一种动态变化混叠模型下欠定盲源分离中的源数估计方法。首先,建立动态变化混叠情形下盲源分离的数学模型及动态标识矩阵。其次,基于构建的动态标识矩阵统计和判断动态源信号数目的变化情况。最后,通过分段时间内多维观测矢量采样点聚类区间局部峰值统计,实现动态变化混叠模型下盲源分离中的源信号数目的有效估计。仿真结果表明,该方法能有效实现动态变化混叠模型下欠定盲源分离中的源数估计,并且信号估计效果良好。     

基于ICA的雷达信号欠定盲分离算法

该文针对源信号时域和频域不充分稀疏的情况,提出了欠定盲源分离中估计混合矩阵的一种新方法。该方法对等间隔分段的观测信号应用独立分量分析(ICA)的盲分离算法获得多个子混合矩阵,然后对其分选剔除了不属于原混合矩阵的元素,最后利用C均值聚类的学习算法获得对混合矩阵的精确估计,解决了源信号在时域和频域不充分稀疏的情况下准确估计混合矩阵的问题。在估计出混合矩阵的基础上,利用基于稀疏分解的统计量算法分离出源信号。由仿真结果,以及与传统的K均值聚类,时域检索平均算法对比的实验结果说明了该文算法的有效性和鲁棒性。     

A Mixing Matrix Estimation Algorithm for Underdetermined Blind Source Separation

This paper considers mixing matrix estimation for underdetermined blind source separation. First, we propose an effective detection algorithm to identify single source points where only one source occurs. The detection algorithm finds single source points by utilizing the time–frequency coefficients of mixed signals and the complex conjugates of the coefficients. Then, a method based on probability density is proposed in order to find more reliable single source points and cluster them. Finally, the mixing matrix is obtained through re-selecting and clustering single source points. The experimental results indicate that the algorithm can accurately estimate the mixing matrix when there are fewer sensors than sources.     

基于时频域单源区域的延迟欠定混合非平稳信号盲分离

针对衰减-延迟欠定混合信号的盲分离问题,提出了基于子空间分解的时频域上单源区域检测方法,估计出信号在时频域上的单源区域以及相应的特征向量,然后利用系统聚类法对单源区域对应的特征向量进行聚类分析,估计出源信号数目以及混合矩阵,最后通过改进的基于子空间投影算法完成源信号的恢复.仿真结果表明本文算法提高了混合矩阵和源信号的估...     

Underdetermined BSS Based on <Emphasis Type="Italic">K</Emphasis>-means and AP Clustering

Underdetermined blind source separation (UBSS) is a hard problem to solve since its mixing system is not invertible. The well-known “two-step approach” has been widely used to solve the UBSS problem and the most pivotal step is to estimate the underdetermined mixing matrix. To improve the estimation performance, this paper proposes a new clustering method. Firstly, the observed signals in the time domain are transformed into sparse signals in the frequency domain; furthermore, the linearity clustering of sparse signals is translated into compact clustering by normalizing the observed data. And then, the underdetermined mixing matrix is estimated by clustering methods. The K-means algorithm is one of the classical methods to estimate the mixing matrix but it can only be applied to know the number of clusters in advance. This is not in accord with the actual situation of UBSS. In addition, the K-means is very sensitive to the initialization of clusters and it selects the initial cluster centers randomly. To overcome the fatal flaws, this paper employs affinity propagation (AP) clustering to get the exact number of exemplars and the initial clusters. Based on those results, the K-means with AP clustering as initialization is used to precisely estimate the underdetermined mixing matrix. Finally, the source signals are separated by linear programming. The experimental results show that the proposed method can effectively estimate the mixing matrix and is more suitable for the actual situation of UBSS.     

基于比率矩阵聚类的欠定盲分离算法

利用稀疏分量的直线聚类性,提出了欠定盲源分离中估计混合矩阵的一种方法。该方法通过构造比率矩阵对观测信号进行分选,剔除了源信号频谱重叠的部分,然后利用鲁棒竞争的聚类学习算法获得对混合矩阵的精确估计,解决了源信号在频域不充分稀疏的条件下准确估计混合矩阵的问题。在估计出混合矩阵的基础上,利用最短路径法分离出源信号。由仿真结果可以看出,与传统的K均值估计混合矩阵的方法相比,方法具有更好的鲁棒性。     

基于JADE和平行因子分解的欠定混合盲辨识算法

针对源信号个数未知的欠定混合盲源分离问题,本文提出了一种基于特征矩阵联合近似对角化（Joint Approximate Diagonalization of Eigenmatrices, JADE）和平行因子分解的欠定混合盲辨识算法,该算法不需要源信号满足稀疏性要求,仅在源信号满足相互独立和最多一个高斯信号的条件下,通过将JADE算法中的样本四阶协方差矩阵叠加成三阶张量,再对此三阶张量进行平行因子分解来完成源信号数和混合矩阵的估计,由于平行因子分解的唯一辨识性在欠定条件下仍然满足,该算法能够解决欠定盲源分离问题。并对该欠定混合盲辨识算法进行了深入的分析。通过仿真实验,计算估计矩阵与混合矩阵的平均相关误差,结果表明本文提出的算法在适定和欠定混合时均具有很好的辨识效果,而且实现简单,可满足实际应用的要求。      

基于谐波提取的欠定语音盲分离方法

现有的欠定语音信号盲分离算法往往不能同时兼顾分离性能及效率。针对此问题,本文提出一种基于谐波提取的欠定盲分离方法。首先,利用频谱校正从混合信号的短时傅立叶变换中提取谐波参数,其次利用相位一致性准则甄别这些参数的单源属性,进而用自适应K-均值方法对单源模式做聚类而获得源数估计和混合矩阵估计,最后再用子空间投影法恢复源信号。其中谐波提取和单源参数筛选可保证低复杂度地精确估计出混合矩阵。仿真实验表明,相比于原始子空间投影算法,本文方法可获得更高的信号恢复质量,且在谐波相关领域也具有潜在应用价值。      

基于方向性模糊C-means与K-means的混合矩阵估计方法

在信源数目未知的欠定盲源分离问题中,精确地估计混合矩阵是具有挑战性的问题。针对现有方法在病态条件下（某些混合向量的方向接近）不能准确估计信源数目、易受离群点干扰的不足,提出了一种基于方向性模糊C-means与K-means的混合矩阵估计方法。该方法首先通过方向性模糊C-means对观测信号进行预聚类,通过预聚类可以实现:1) 根据聚类有效性指标值的收敛点确定信源数目;2）根据隶属度矩阵排除离群点;3）确定K-means的初始聚类点。最后使用K-means并利用预聚类确定的信源数目及初始聚类点实现混合矩阵估计。仿真结果表明提出的方法具有更优的混合矩阵估计性能。      

具有延迟的欠定语音盲分离

探讨具有延迟的欠定语音盲分离问题,针对语音信号的部分W-分离正交性,提出一种新的基于混叠矩阵估计的语音盲分离方法.首先对观测信号进行短时傅里叶变换,选定一个信号作为参考信号,构造幅度衰减向量和时间延迟向量,提取单源主导区间的观测信号作为观测样本;然后对观测样本进行聚类,通过估计参考信号的混叠系数来估计混叠矩阵;最后结合...     

欠定线性瞬时混合盲分离矩阵求解算法

针对欠定线性瞬时混合中的混合矩阵条件数较大的情况,使用最小二乘估计算法求解源信号造成的噪声放大问题,研究了一种求解分离矩阵的算法。此方法基于最大信干噪比的原则建立代价函数,通过最优化此函数得到分离矩阵。仿真实验表明,该算法与最小二乘算法相比可以改善在混合矩阵条件数较大时噪声放大影响下的分离性能。     

Underdetermined blind separation of non-disjoint signals in time-frequency domain based on matrix diagonalization

To estimate precisely the mixing matrix and extract the source signals in underdetermined case is a challenging problem, especially when the source signals are non-disjointed in time-frequency (TF) domain. The conventional algorithms such as subspace-based achieve blind source separation exploiting the sparsity of the original signals and the mixtures must satisfy the assumption that the number of sources that contribute their energy at any TF point is strictly less than that of sensors. This paper proposes a new method considering the uncorrelated property of the sources in the practical field which relaxes the sparsity condition of sources in TF domain. The method shows that the number of the sources that exist in any TF neighborhood simultaneously equals to that of sensors. We can identify the active sources and estimate their corresponding TF values in any TF neighborhood by matrix diagonalization. Moreover, this paper proposes a method for estimating the mixing matrix by classifying the eigenvectors corresponded to the single source TF neighborhoods. The simulation results show the proposed algorithm separates the sources with higher signal-to-interference ratio compared to other conventional algorithms.     

基于三阶统计量的欠定盲源分离方法

盲源分离(BSS)在缺失源信号信息及信息混合方式信息的情况下,仅利用观测信号实现源信号恢复,是信号处理中的重要手段。欠定盲源分离(UBSS)中观测信号少于源信号数目,因此,相较于正定/超定情形,其更接近现实情况。然而,观测信号往往受到噪声干扰,传统基于2阶统计量和信号稀疏性的欠定盲源分离结果对噪声较为敏感。鉴于3阶统计量在处理对称分布噪声时的优势,该文利用观测信号的3阶统计信息实现混合矩阵的估计。考虑到源信号的自相关特性,计算多时延下观测信号一系列的3阶统计信息,并堆叠成4阶张量,进而将混合矩阵估计问题转化为4阶张量的典范双峰分解问题。该文进一步利用广义高斯模型和期望最大算法实现源信号的恢复。1000次蒙特卡罗实验表明该文算法能够有效抑制噪声的影响。针对3×4混合模型,当信噪比为15 dB时,该文算法对混合矩阵的平均估计误差达到–20.35 dB,所恢复出的源信号与真实源信号之间的平均绝对相关系数达0.84,与现有方法相比,取得了最好的分离结果。     

Mixing matrix estimation method for dual‐channel time‐frequency overlapped signals based on interval probability

For dual‐channel time‐frequency (TF) overlapped signals with low sparsity in underdetermined blind source separation (UBSS), this paper proposes an effective method based on interval probability to estimate and expand the types of mixing matrices. First, the detection of TF single‐source points (TF‐SSP) is used to improve the TF sparsity of each source. For more distinguishability, as the ratios of the coefficients from different columns of the mixing matrix are close, a local peak‐detection mechanism based on interval probability (LPIP) is proposed. LPIP utilizes uniform subintervals to optimize and classify the TF coefficient ratios of the detected TF‐SSP effectively in the case of a high level of TF overlap among sources and reduces the TF interference points and redundant signal features greatly to enhance the estimation accuracy. The simulation results show that under both noiseless and noisy cases, the proposed method performs better than the selected mainstream traditional methods, has good robustness, and has low algorithm complexity.     

Compressed Blind Signal Reconstruction Model and Algorithm

The model of inherent connection between underdetermined blind signal separation and compressed sensing (CS) is analyzed first; then, the mathematical model of underdetermined blind signal reconstruction is built using CS. More specifically, the mixing matrix is estimated by exploiting the wavelet packet transform and k-means clustering methods up to permutation and scaling indeterminacy, and then, the measurement matrix and the measurement equation are obtained. To reconstruct the underdetermined sparse source signals, the proposed semi-blind compressed reconstruction algorithm is derived based on the blind signal reconstruction model and compressive sampling matching pursuit (CoSaMP) method. Our simulation results demonstrate that the proposed scheme is effective, irrespective of artificial data or real data. Moreover, the proposed scheme can be adjusted for different applications by modifying the mixing matrix estimation method and CoSaMP method with respect to the correspondence conditions.     

An anti‐repeater‐jamming approach based on blind source separation for the downlink of satellite communication systems

In this paper, an anti‐jamming approach is proposed for the downlink of satellite communication systems when encountering a hostile repeater‐jamming. Based on blind source separation, this approach can eliminate repeater‐jamming by separating the mixtures of the communication signals and the repeater‐jamming. Meanwhile, oversampling method is employed to transform the underdetermined mixing of signals into a determined mixing for facilitating the separation. In the simulations, the symbol error ratio (SER) of the separated communication signals can approximate the theory SER, and the anti‐repeater‐jamming capacity can arrive to nearly 28 dB.     

一种欠定盲源分离中混合矩阵的估计方法

欠定盲源分离问题中基于源信号稀疏性的两阶段法中,混合矩阵估计的准确与否,直接影响源信号的恢复效果。文中提出了一种在稀疏域估计混合矩阵的新方法。该方法通过搜索稀疏域中同一直线附近的点,利用这些点重构出混合矩阵,避免了远离直线周边的点对估计混合矩阵的干扰,从而大大降低了计算量。仿真表明该算法性能良好。     

快速NMF盲源分离算法

将秩一非负矩阵分解应用于盲源分离问题,把基于欧式距离的目标函数转化成二次函数的形式;施加稀疏性约束和正交性约束保证信号可分离性;利用二次函数的性质分别推得混合矩阵和源信号的迭代公式,从而得到一种基于秩一分解的快速NMF盲源分离算法（NMF-R1)。分析得到一次迭代更新NMF-R1算法比传统NMF盲源分离算法（NMF-BM)所需乘法次数少约30%,NMF-R1算法无矩阵求逆运算,NMF-BM算法还需2次矩阵求逆运算。图像信号的超定和欠定盲源分离仿真结果表明,NMF-R1算法都能分离出源信号, NMF-BM算法只能分离超定混合信号;NMF-R1算法与NMF-BM算法比,分离性能好、收敛速度快。      

基于时频分布的欠定混合矩阵盲辨识

针对欠定混合矩阵的盲辨识问题,提出了基于空间时频分布的盲辨识算法,首先计算信号的空间时频分布并找出源信号的自源时频点,然后把所有自源点对应的时频分布矩阵表示成高维矩阵的形式,再通过联合对角化和特征值分解估计出混合矩阵.该方法不需要假设源信号是稀疏的或独立的,此外通过检测能量足够大的自源时频点,提高了算法的鲁棒性.仿真结...