基于压缩感知的欠定盲分离源信号恢复算法研究

发布时间：2018-03-24 19:42

本文选题：欠定盲分离　切入点：压缩感知　出处：《西安电子科技大学》2015年硕士论文

【摘要】：欠定盲分离指对源信号及信道参数一无所知的情况下,仅仅根据传感器接收到的信号直接将源信号恢复出来。压缩感知是近年来发展起来的一门压缩采样技术,它能以低于奈奎斯特采样速度的采样率对信号进行采样,并且在接收端对源信号进行近乎完美的恢复。由于压缩感知稀疏信号重构与欠定盲分离中的源信号恢复有相同的数学模型,因此,压缩感知稀疏信号重构算法被广泛的用来解决欠定盲分离源信号恢复问题。本文研究的就是基于压缩感知的欠定盲分离源信号恢复技术。本文的工作可以概括为如下几个方面:(1)指出了Pando Georgiev等提出的欠定盲分离可完全重构条件所存在的问题,对结论进行了完善。通过对Pando Georgiev等提出的欠定盲分离可完全重构条件与压缩感知中的NSP准则进行对比,发现了结论的不一致性,找出了欠定盲分离可完全重构条件存在的问题,对结论进行了修正。(2)针对贪婪算法中的互补匹配追踪算法复杂度较高的问题,提出了子空间互补匹配追踪算法。贪婪算法是一种在源信号充分稀疏的条件下性能较好的算法。贪婪算法中时间复杂度较低的匹配追踪算法恢复精度较低,而精度较高的互补匹配追踪算法复杂度又较高。针对此问题,本文在互补匹配追踪算法的基础上,结合子空间搜索的思想,提出了子空间互补匹配追踪算法。提出的算法在显著减小算法时间复杂度的基础上,在一定程度上提高了算法的精度,体现出了良好的性能。(3)针对基于L1范数的稀疏信号重构算法复杂度较高的问题,提出了基于L1范数的互补匹配追踪算法。现有的基于L1范数的稀疏信号重构算法存在的问题是复杂度普遍较高,针对此问题,本文将原始优化问题进行了降维处理,利用迭代收敛方法求解问题的最优解。通过理论分析和仿真实验得出,该算法在显著降低算法复杂度的同时,保持了原有算法的精度。(4)针对平滑L0范数收敛速度慢以及受步长影响较大的问题,提出了基于修正牛顿法的径向基函数算法。该算法将修正牛顿法引入到了径向基函数算法当中,克服了原始的径向基函数算法恢复精度受步长影响较大的问题,通过仿真得出,改进的算法在显著降低算法复杂度的同时,也提高了算法的精度。
[Abstract]:Undetermined blind separation refers to recovering the source signal directly from the signal received by the sensor without knowledge of the source signal and channel parameters. Compression sensing is a compression sampling technique developed in recent years. It can sample the signal at a rate lower than Nyquist's. And the source signal is restored almost perfectly at the receiving end. Because the reconstruction of compressed perceptual sparse signal has the same mathematical model as the source signal recovery in under-determined blind separation, so, Compressed sensing sparse signal reconstruction algorithm is widely used to solve the problem of undetermined blind source signal recovery. In this paper, we study a compressed perceptual algorithm for the restoration of underdetermined blind separated source signals. The work of this paper can be summarized as follows. The following are several aspects: 1) We point out the problem of the condition that Pando Georgiev et al can completely reconstruct the undetermined blind separation. The conclusion is improved. By comparing the fully reconfigurable condition of underdetermined blind separation proposed by Pando Georgiev and the NSP criterion in compression perception, the inconsistency of the conclusion is found, and the problems existing in the fully reconfigurable condition of under-determined blind separation are found out. The conclusion is modified to solve the problem of high complexity of complementary matching tracking algorithm in greedy algorithm. A subspace complementary matching tracking algorithm is proposed. Greedy algorithm is a better algorithm with sparse source signal. The algorithm with low time complexity in greedy algorithm has low recovery accuracy. The complexity of complementary matching tracking algorithm with high precision is higher. In order to solve this problem, this paper combines the idea of subspace search based on complementary matching tracking algorithm. A subspace complementary matching tracking algorithm is proposed, which can significantly reduce the time complexity of the algorithm and improve the accuracy of the algorithm to a certain extent. It shows good performance. (3) aiming at the problem of high complexity of sparse signal reconstruction algorithm based on L1 norm, This paper presents a complementary matching tracking algorithm based on L1 norm. The existing sparse signal reconstruction algorithm based on L1 norm has a high complexity. In view of this problem, the original optimization problem is reduced by dimension reduction. The iterative convergence method is used to solve the optimal solution of the problem. The theoretical analysis and simulation results show that the algorithm can significantly reduce the complexity of the algorithm at the same time. In order to solve the problem of slow convergence speed of smooth L0 norm and large influence of step size, the accuracy of the original algorithm is maintained. A radial basis function algorithm based on modified Newton method is proposed. The modified Newton method is introduced into the radial basis function algorithm, which overcomes the problem that the restoration accuracy of the original radial basis function algorithm is greatly affected by step size. The improved algorithm can significantly reduce the complexity of the algorithm, but also improve the accuracy of the algorithm.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN911.7

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