Research On Distributed Compressive Sensing Of Instantaneous Mixture Signals

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.