基于SWCoSaMP算法的稀疏信号重构

压缩感知(compressed sensing, CS)稀疏信号重构本质上是在稀疏约束条件下求解欠定方程组。针对压缩感知匹配追踪(compressed sampling matching pursuit, CoSaMP)算法直接从代理信号中选取非零元素个数两倍作为支撑集,但是不存在迭代量化标准,本文提出了分步压缩感知匹配追踪(stepwise compressed sampling matching pursuit, SWCoSaMP)算法。该算法从块矩阵的逆矩阵定义出发,采用迭代算法得到稀疏信号的支撑集,推出每次迭代支撑集所对应重构误差的L-2范数闭合表达式,从而重构稀疏信号。实验结果表明和原来CoSaMP算法相比,对于非零元素幅度服从均匀分布和高斯分布的稀疏信号,新算法具有更好的重构效果。      

不同压缩感知重建算法在鬼成像中的性能比较

基于鬼成像(Ghost imaging,GI)与压缩感知(Compressed sensing,CS)理论,研究了CS重建算法对GI成像性能的影响.以离散小波变换为图像的稀疏矩阵、具有高斯线型的热光源强度分布为测量矩阵,分析了基于增广拉格朗日法和交替方向法的全变分最小化算法(TVAL3)、正交匹配追踪算法(OMP)、压缩采样匹配追踪算法(CoSaMP)、梯度投影算法(GPSR_Basic)下的压缩鬼成像的质量.以均方误差、峰值信噪比、匹配度、结构相似性指标等为图像质量客观评价标准,比较了4种重建算法下压缩鬼成像的重建结果.结果表明压缩比为0.5时TVAL3算法还原度最高, CoSaMP算法重建图像失真最严重, GPSR_Basic算法获得的重建性能优于OMP算法.     

基于随机滤波的探地雷达成像方法

探地雷达是一种超宽带雷达系统,若按传统的奈奎斯特采样,雷达回波信号需要大量空间存储。压缩感知可以实现利用少量的测量值对稀疏信号进行重构,其中最为关键的是测量矩阵和重构算法的选择。本文将压缩感知应用于探地雷达成像,并利用随机滤波的思想选择测量矩阵,可以有效减少测量矩阵中非零值的个数。利用正交匹配追踪算法对信号进行重构,算法简单,降低了数据的存储量和运算复杂度,该算法同样可以对时间和空间上同时压缩的数据进行成像。最后,本文给出基于时间连续信号的GPR接收机一种CS实现方案。仿真结果表明,本文提出的成像方法可以以少量数据精确地对信号进行重构,并且运算量少。      

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。     

利用DBSCAN和概率密度估计的欠定盲源分离混合矩阵估计

针对欠定盲源分离中混合矩阵估计精度不佳的问题,本文提出了一种结合带噪声的基于密度的空间聚类（combining density-based spatial clustering of application with noise, DBSCAN）和概率密度估计的混合矩阵估计算法。首先,通过向量转换方式获得单声源时频点检测准则,并基于此准则从混合信号中检测出单声源点。其次,利用基于密度的空间聚类算法对单声源点进行聚类,由此估计出声源个数以及各类别所属的单声源点。再次,利用概率密度估计获得各类别的聚类中心,并构成混合矩阵。所提混合矩阵估计方法不需要提前设定声源个数,并且避免了由于数据分布不均所造成的聚类效果差的问题。最后,采用压缩感知技术实现源信号恢复,从而从混合信号中分离出各个声源信号。实验结果表明,本文所提的混合矩阵估计方法在声源个数未知的情况下,能够准确估计出混合矩阵;并且分离出的信号具有较高的质量。     

基于基追踪-Moore-Penrose逆矩阵算法的稀疏信号重构

压缩感知(Compressed Sensing,CS)稀疏信号重构其本质就是在稀疏约束条件下求解欠定线性方程组,基于迭代加权L-p(0＜p≤1,p=2)类范数算法减小重构误差成为近来稀疏信号重构热点之一.该文提出了基追踪-Moore-Penrose逆矩阵(Basis Pursuit-Moore-Penrose Inverse Matrix,BP-MPIM)算法:(1)由基追踪(Basis Pursuit,BP)算法得到稀疏信号非零元素位置(亦称支撑集,对应于测量矩阵的列);(2)通过求解由支撑集所对应测量矩阵的子矩阵和CS测量值组成的超定线性方程组实现稀疏信号重构,并证明了由此重构的稀疏信号是其唯一最小二次范数解.仿真的稀疏信号和实测宽带雷达回波信号脉冲压缩结果表明,和原来算法相比,新算法具有更小的重构误差,且误差只存在于其支撑集内.     

弱稀疏语音信号的欠定盲分离

为解决弱稀疏语音信号的欠定盲分离问题,根据语音信号的部分W-分离正交性,提出一种基于单源主导区间的混合矩阵盲估计方法。该方法根据单源主导区间的性质,通过二元行矢量提取单源观测样本,对单源观测样本进行K均值聚类和主成分分析来估计混合矩阵。仿真结果表明,提出的方法可有效提高分离语音的性能,与直接利用K-PCA方法相比,分离语音的平均信噪比提高了10 dB左右。     

One-bit compressed sensing recovery algorithm robust to perturbation

One-bit compressed sensing(CS) technology reconstructs the sparse signal when the available measurements are reduced to only their sign-bit. It is well known that CS reconstruction should know the measurement matrix exactly to obtain a correct result. However, the measurement matrix is probably perturbed in many practical scenarios. An iterative algorithm called perturbed binary iterative hard thresholding (PBIHT) is proposed to reconstruct the sparse signal from the binary measurements (sign measurements) where the measurement matrix experiences a general perturbation. The proposed algorithm can reconstruct the original data without any prior knowledge about the perturbation. Specifically, using the ideas of the gradient descent, PBIHT iteratively estimates signal and perturbation until the estimation converges. Simulation results demonstrate that, under certain conditions, PBIHT improves the performance of signal reconstruction in the perturbation scenario.     

基于压缩感知的超分辨目标散射中心估计

针对雷达目标识别中散射中心特征提取需求,提出一种基于压缩感知理论(CS)的超分辨散射中心估计算法。通过设计一字典,将脉压波形进行稀疏表示,进而将重构问题引入CS 理论框架之下,利用仿真数据验证了散射中心重构算法的可行性。基于实录数据,将80 MHz 宽带信号滤波成20 MHz 窄带信号,利用窄带20 MHz 脉压波形重构高分辨散射中心,进而恢复宽带80 MHz 脉压信号。恢复信号与真实80 MHz 宽带脉压信号的对比分析结果表明,在一定误差范围内,CS算法可实现目标散射中心重构。     

适用于压缩感知估计角度的测量矩阵研究

针对接收数据压缩投影后导致到达角 (Direction-Of-Arrival, DOA)估计精度不高的问题,提出一种高精度的全局信息压缩投影到达角估计算法。该算法首先提出更适应角度估计的空域稀疏化范德蒙矩阵作为测量矩阵,然后对由其组成的Gram矩阵的非对角元素进行压缩处理得到目标矩阵,接着利用步长符合沃尔夫条件的梯度下降法优化Gram矩阵,得到当Gram矩阵与目标矩阵最接近时所对应的可以保留更多全局信息的测量矩阵,最后利用此矩阵压缩接收数据,将接收数据投影到测量矩阵空间,进行稀疏重构得到角度估计结果。仿真实验表明,所提算法角度估计精度远优于同等条件下辐射源信号直接重构的角度估计结果,且在信噪比大于-6dB时数据压缩投影后角度估计的成功率达到100%,性能优越。      

基于压缩感知的欠定图像盲源分离研究

系统阐述了利用稀疏成分分析(Sparse Component Analysis,SCA)算法进行欠定图像盲源分离。首先在估计出源图像个数的基础上,利用线性聚类估计混合矩阵;其次将压缩感知(Compressed Sensing,CS)应用到恢复源图像中。为了得到自适应的过完备稀疏字典来提高分离效果,提出了利用K均值奇异值分解(K-means Singular Value Decomposition,K-SVD)算法对过完备DCT字典循环迭代训练的思想,并对图像分块处理来减少计算复杂度;最后进行了仿真测试并对分离出的图像进行了分析和进一步处理。     

欠定和非完全稀疏性的盲信号提取

两步策略已成为欠定盲信号分离的基本方法,混叠矩阵的估计是源恢复的先决条件.本文针对非完全稀疏性情况,提出一个两步的盲提取方法.该方法先利用信号的单源区间样本,估计部分源的基矢量（混叠矩阵的列矢量）,后最小干扰地提取所对应的源;除它所对应的基矢量外,它不依赖的其它的基矢量,故回避了混叠矩阵可识别的必要条件.几个仿真实验结果显示了该算法的性能和实用性.     

基于超平面法矢量的欠定盲混合矩阵估计

源信号稀疏性差时,基于源信号稀疏特性的欠定盲混合矩阵估计算法,通常先聚类求得混合矢量张成的超平面,然后估计混合矩阵。但此方法涉及运算量较大的超平面聚类,算法效率低。针对这一缺陷,提出了一种新的混合矩阵估计算法。先由所提出的基于梯度法的法矢量更新方法求得超平面法矢量的估计,然后求出混合矩阵。该方法不需要进行超平面聚类,大大降低了运算量,提高了混合矩阵估计效率。仿真结果证明了该方法的正确性和有效性。     

A distributed compressed sensing approach for speech signal denoising

Compressed sensing, a new area of signal processing rising in recent years, seeks to minimize the number of samples that is necessary to be taken from a signal for precise reconstruction. The precondition of compressed sensing theory is the sparsity of signals. In this paper, two methods to estimate the sparsity level of the signal are formulated. And then an approach to estimate the sparsity level directly from the noisy signal is presented. Moreover, a scheme based on distributed compressed sensing for speech signal denoising is described in this work which exploits multiple measurements of the noisy speech signal to construct the block-sparse data and then reconstruct the original speech signal using block-sparse model-based Compressive Sampling Matching Pursuit (CoSaMP) algorithm. Several simulation results demonstrate the accuracy of the estimated sparsity level and that this denoising system for noisy speech signals can achieve favorable performance especially when speech signals suffer severe noise.     

Underdetermined mixing matrix estimation bycomprehensive application of cluster validity indexes

To solve the problem of mixing matrix estimation for underdetermined blind source separation (UBSS) when thenumber of sources is unknown, this paper proposed a novel mixing matrix estimation method based on averageinformation entropy and cluster validity index (CVI). Firstly, the initial cluster center is selected by using fuzzy C-means (FCM) algorithm and the corresponding membership matrix is obtained, and then the number of clusters isobtained by using the joint decision of CVI and average information entropy index of membership matrix, thenmultiple cluster number estimation results can be obtained by using multiple CVIs. Then, according to the results ofthe number of multiple clusters estimation, the number of radiation sources is determined according to the principleof the subordination of the minority to the majority. The cluster center vectors obtained from the clustering operationof the estimated number of radiation sources are fused, that is the mixing matrix is estimated based on the degree ofsimilarity of the cluster center vectors. When the source signal is not sufficiently sparse, the time-frequency singlesource detection processing can be combined with the proposed method to estimate the mixing matrix. Theeffectiveness of the proposed method is validated by experiments.     

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.     

Improved statistical sparse decomposition principle method for underdetermined blind source signal recovery

Aiming at the statistical sparse decomposition principle (SSDP) method for underdetermined blind source signal recovery with problem of requiring the number of active signals equal to that of the observed signals, which leading to the application bound of SSDP is very finite, an improved SSDP (ISSDP) method is proposed. Based on the principle of recovering the source signals by minimizing the correlation coefficients within a fixed time interval, the selection method of mixing matrix's column vectors used for signal recovery is modified, which enables the choose of mixing matrix's column vectors according to the number of active source signals self-adaptively. By simulation experiments, the proposed method is validated. The proposed method is applicable to the case where the number of active signals is equal to or less than that of observed signals, which is a new way for underdetermined blind source signal recovery.     

行阶梯观测矩阵下语音压缩感知观测序列的Volterra+Wiener模型研究

针对压缩感知理论下,语音信号经随机高斯矩阵投影后得到的观测序列随机性太强,难以建模的问题,提出了一种基于行阶梯观测矩阵的语音压缩感知观测序列的Volterra模型,利用该模型实现对语音压缩感知观测序列的预测,研究了Volterra滤波器输入维数与阶数对预测效果的影响,并利用维纳滤波器进一步降低预测误差。在相同的已知数据量下,基于部分压缩感知观测序列、Volterra模型、Wiener滤波器的重构,获得了优于高斯随机观测序列的重构性能。模型的研究为压缩感知与语音技术的结合提供一定的参考价值。      

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...     

基于线性混合模型的高光谱图像谱间压缩感知重构

该文针对高光谱数据的线性混合模型,提出一种简单有效的谱间压缩感知下高光谱数据的重构方案。该方案不同于传统的压缩感知重构方法直接重构高光谱数据,而是将高光谱数据分离成端元和丰度分别进行重构,然后利用重构的端元和丰度信息合成高光谱数据。实验结果表明,该方案的重构质量明显优于标准压缩感知重构方法,并且运算速度具有极大提升,同时便于获得端元和丰度信息。