【作者】 于伟；

【导师】 付宁；

【作者基本信息】 哈尔滨工业大学 ， 仪器科学与技术， 2013， 硕士

【摘要】 压缩感知（Compressed Sensing，CS）理论以其特有的采样方式，突破了传统的奈奎斯特采样的限制，近几年在信号处理领域引起了广泛的关注。分布式压缩感知（Distributed Compressive Sensing，DCS）将压缩感知理论扩展到了多个传感器信号的场合，在信号重构算法中考虑了多个通道信号之间的相关性，进一步提高了信号的压缩效率，在很多领域具有广泛的应用前景。然而，在一些多传感器信号的分布式压缩感知场合，很难真实地检测到源信号，各传感器接收到的信号往往是多种源信号的一种混合。目前，该方向的研究起步较晚，还没有比较成熟的理论和方法，本文针对分布式压缩感知中的线性瞬时混合信号问题展开研究，主要研究内容和取得的成果如下：1、分析瞬时混合信号之间的相关性，从重构混合信号的角度展开研究。首先介绍了信号的混合模型，而后分析了混合信号的分布式压缩观测模型，并详细的介绍了分布式压缩感知中联合稀疏模型的特点。在分析了瞬时混合信号之间的相关性之后，推导了瞬时混合信号的联合稀疏模型，并将DCS中的DCSSOMP算法应用到瞬时混合信号的联合重构过程中。最后，通过仿真实验验证了该算法重构瞬时混合信号的效果，实验结果表明，重构瞬时混合信号时采用联合重构算法的精度优于单通道分别重构的精度。2、分析源信号压缩观测值的统计特性，从重构源信号的角度展开研究。首先详细介绍了独立分量分析的原理，在分析了源信号压缩观测值、混合信号压缩观测值的独立性以及非高斯性的基础上，提出了一种基于压缩观测值独立性的源信号重构算法，该算法首先在压缩域采用独立分量分析的方法从混合信号的压缩观测值中分离出源信号的压缩观测值，然后通过CS重构算法重构出源信号。该算法避免了重构混合信号的过程，从混合信号的压缩域直接分离源信号观测值。最后通过仿真实验验证了本文算法的有效性，实验结果表明，与现有的DCSSOMP-SS算法、OMP-SS算法相比，本文算法具有更高的重构精度。3、研究模拟瞬时混合信号的分布式压缩感知方法。在本文中采用目前比较流行的一种模拟信息转换器——随机解调，实现对混合信号的压缩采样。首先研究了随机解调的工作原理，并分析了随机解调中低通滤波器参数非理想特性对信号重构精度的影响。然后，研究了随机解调采样框架下，模拟混合信号的分布式压缩感知方法，对联合重构算法重构混合信号进行了仿真，最后分析了随机解调采样值的独立性、非高斯性，并通过仿真实验比较在随机解调压缩采样框架下，基于压缩观测值独立性的源信号重构算法、DCSSOMP-SS算法、OMP-SS算法的重构效果，验证本文算法在随机解调采样框架下的有效性和实用性。更多还原

【Abstract】 Compressed sensing (CS) has attracted wide attention in signal processingrecently years. Due to its unique sampling theory, the sampling rate can be slowthan the nyquist frequency of the signals. Distributed compressed sensing (DCS),which is an important branch of CS, expand the CS theory to the multi-signalsensembles. DCS uses the correlation structures of signals in recovery algorithms,and get a better reconstruction. So it has abroad application in many areas.While in some distributed compressed sensing for multi-siganls, the sourcesignals are unavailable for observation. The signals collected by each sensor wouldbe a mixture of the real source signal and other useless signals. In this case, itcannot recover the source signals by the reconstruction algorithm in CS. While theinformation of the source signals always be an important basis for further decisions.So it is an urgent problem to recover the source signals from the compressivemeasurements of mixture signals.One of the methods to solve the aboved problem is reconstructing the mixturesignal first, and then separating the source signals from the mixture signals. Mostresearchs of this method adopt the CS reconstruction algorithms to recover mixturesignals, which neglect the correlation of the mixture signals between each sensor.The other method is to recover the source signals directly from the measurements ofmixture signals. While only a few scholars had got some achievement, and themethods are not enough to solve the problem.This dissertation focus on the problem of mixture signals in the DCS. Themain contents and research contributions of this paper are listed as follows:1. The model of signals and the joint reconstruction algorithm of mixturesignals are studied. The mixing model are decribed detailed first. In this paper onlythe instantaneous linear mixing model are considered. Next, we introduct thedistributed compressive sensing model for mixture signals and the joint sparsemodel (JSM) mentioned in DCS. After analyse the correlation of the mixturesignals, the JSM of mixture signals is infered. Then, a joint reconstructionalgorithm called DCS-simultaneous orthogonal matching pursuit (DCSSOMP) isemployed to the recovery of mixture signals. In the simulate experiments, a jointreconstruction used DCSSOMP algorithm has a better accuracy than the separate reconstruction with orthogonal matching pursuit (OMP).2. Consider the recovery of source signals directly from the measurements.The independent component analysis (ICA) theory is showed first. After analyse theindependence and nongaussianity of the compressive measurements, a source signalrecovery algorithm based on independence is proposed in this paper. In thisalgorithm, independent component analysis is adopted to separate the sourcesignals’ compressive measurements from the measurements of mixture signals. Usethe OMP algorithm to reconstruct the source signals from their compressivemeasurements. In the numerical experiments, use audio signal as the source signal.The results show that the proposed method has a better performance than theDCSSOMP-SS and OMP-SS algorithms in recovering the source signals.3. Focus on the DCS methods for analog mixture signals. In this paper, randomdemodulator (RD), a common compressive sampling structure of analog-to-information convertor (AIC), is applied to the sampling of mixture signals. Fisrtstudy the theory of the random demodulator. And the effect for signalsreconstruction caused by the non-ideal of the low pass filter is discussed throughnumerical experiments. Then the independence and nongaussianity of the RDsampling measurements are analysed. Simulation results demonstrate that the jointreconstruction for mixture signals and the source recovery algorithm based onindependence have a good performance under the random demodulator samplingstructure.更多还原