Research On Multichannel Compressive Sensing Based Information Extraction Methods

As the development of electronic and information technologies, the frequency of a signal becomes higher and higher, as well as the undistorted sampling rate, which brings big challenges to the design of sampling system, data transmission, data storage and so on. Compressive Sensing(CS) theory brings hope for solving this problem. CS indicates that when a signal is sparse itself or in some basis, it can be recovered exactly from a few number of samples, much less than the number required by traditional sampling methods. Multichannel CS extends CS theory from one signal to multiple signals so as to recover all the signals jointly. In some applications, target signals can be sampled directly. While in many other applications, the sampled signals are mixing signals, mixtures of several sources. Sources and mixing parameters should be extracted from mixtures. Based on the research of Multichannel CS, the problems of extraction speed and extraction accuracy are analyzed, and extraction methods of information from compressed samples of sources or mixtures are studied. The main research work is as follows.Firstly, in the joint sparse model that has common sparse part, the computational complexity of greedy algorithms when recovering non-mixed signals is very high. Most existing methods transform Multichannel CS problem to single-channel CS problem, reduce the redundancy among signals, and recover signals by greedy algorithms. When the number of signals is big, the recovery speed of the methods mentioned above is very slow. Based on the mentioned me thods, a fast information extraction method is proposed to reduce the computational complexity of most existing greedy algorithms. By taking advantage of sparse feature of a joint measurement matrix, the matrix is divided into several full-zero and non-zero submatrices. This research reduces the computational complexity of matching operation by using only non-zero submatrices for calculation. It is noted that the recovery accuracy of greedy algorithms is not changed while improves the recovery speed, because the result of matching operation is not changed.Secondly, this research aims to improve both the extraction speed of mixing parameters and the extraction accuracy of independent sources from compressed measurements of mixtures. Traditional methods recover mixtures from the observations and extract mixing parameters and sources from the recovered mixtures sequentially. Based on the preconditions that the compressed measurements of sources are independent and non-Gaussian, Compressive Independent Component Analysis(CICA) method is proposed, which extracts the mixing parameters and compressed measurements of sources directly from compressed measurements of mixtures by Independent Component Analysis(ICA) method, and sources are extracted from their compressed measurements in a further step. Audio signals are used in the experiments. Experiment results demonstrate that both the extraction speed and extraction accuracy of mixing parameters of CICA method are better than those of traditional methods, due to omitting the step of recovering mixtures. And the extraction accuracy of sources is also better.Thirdly, when sources are non-independent and non-negative, this research presents a method to improve the extraction speed of mixing parameters from compressed measurements of mixtures. By using non-negative and sum-to-one conditions of sources, Compressive Endmember Extraction(CEE) method is proposed. In this method, sufficient conditions that the measurement matrix should satisfies, when extracting mixing parameters by Convex Geometry(CG) method directly from compressed measurements of mixtures, are deduced. The conditions are that each row of the measurement matrix should be non-negative and sum-to-one. Based on these conditions, CEE method extracts mixing parameters directly from compressed measurements of mixtures, omitting the step of recovering mixtures. The computational complexity of CEE is lower than the computational complexity of traditional methods, which recover mixtures and extract mixing parameters sequentially. And the extraction speed of CEE is faster. Hyperspectral images are used in the experiment. The experiment results indicate that the endmember(mixing parameters) extraction accuracy of CEE is better under the condition that pure pixels of each endmember exist in the compressed measurements of abundance.