基于贝叶斯压缩感知的块状稀疏信号恢复算法研究

发布时间：2018-06-01 14:04

  本文选题：稀疏贝叶斯学习 + 结构配对层次模型　； 参考：《电子科技大学》2014年硕士论文

【摘要】：本文主要考虑了块状稀疏(block-sparse)信号的恢复问题,利用压缩感知理论,通过挖掘信号的稀疏特性及块状聚类结构特性,基于低维的测量量来恢复高维的信号。这样的方案可以在保证信号恢复精度的同时,有效的降低恢复信号所需的测量量。本文主要考虑的场景是,稀疏信号的非零系数是呈块状聚类的形式出现的,但是其非零块的位置和大小是未知的。通过贝叶斯学习的方法,构建层次化高斯先验模型,来恢复块状稀疏信号。本文首先在噪声方差已知的条件下,采用基于结构配对的层次化高斯先验模型来表征信号系数间的统计相关性,采用一组超参数(hyperparameter)来控制信号的稀疏性。传统贝叶斯学习方法中,每个超参数都单独的控制其对应的信号系数的性质。与传统的贝叶斯稀疏学习方法不同,本文中提出的基于结构配对的压缩感知恢复算法中,每个信号稀疏的先验分布,不仅与自身对应的超参数有关,而且与其相邻系数的超参数有关,这样的基于结构配对的参数化模型,可以将相邻系数关联起来,因此,这样的结构可以有效的促进信号的块状聚类特征,挖掘信号块状先验。在这样的高斯先验模型下,采用期望最大化(expectation-maximization)算法,通过循环迭代,恢复块状信号。同时,本文还考虑了在噪声方差未知的情况下的信号恢复,在这种情况下,将信号看做隐藏参数,并同样采用期望最大化的方法,依次迭代出估计信号及噪声方差的值,从而实现对稀疏信号的恢复。文中还进一步介绍了一种基于结构配对的改进重加权优化算法,这种算法同样可以在未知信号分块结构和稀疏度的前提下,挖掘信号内在块状聚类信息,利用较少的测量量,有效的恢复信号。文章还进一步研究了时变稀疏信号的恢复,即不再仅仅考虑单一时隙稀疏信号恢复,而是考虑多时隙测量向量的情况。但是与传统多测量向量的情况不同,本文中考虑的多测量信号的稀疏结构不再是随时间恒定不变的,因为在很多情况下,稀疏信号的非零系数位置,是随时间发生缓慢变化的,在本文中,我们就研究了这一问题模型下的信号恢复问题,采用的主要方法是将时变稀疏信号模型通过数学变换,转化为块结构未知的块稀疏信号的恢复问题进行恢复。仿真结果表明通过挖掘信号的稀疏性以及块状特征,利用本文提出的基于结构配对的层次化高斯模型,可以有效的恢复块状稀疏信号,在噪声方差已知时,信号可以以很高的概率完全恢复。而在存在噪声,且噪声方差未知时,也可以对信号实现有效恢复。对自然数据,如图像、声音数据的仿真也表明,自然界的很多信号都具有这样的块状稀疏特征,且可以利用本文提出的算法进行有效恢复。另一方面,对DoA模型中时变信号的恢复,同样表明本文所提出算法对于时变信号的恢复也具有比较好的效果。
[Abstract]:In this paper, the recovery problem of block-sparsed-block signals is mainly considered. Using the theory of compression perception, the high-dimensional signals are recovered based on low-dimensional measurements by mining the sparse characteristics of the signals and the structural characteristics of block-like clustering. This scheme can effectively reduce the amount of measurement needed to restore the signal while ensuring the accuracy of the signal recovery. The main scenario considered in this paper is that the non-zero coefficients of sparse signals appear in the form of block clustering but the position and size of the non-zero blocks are unknown. A hierarchical Gao Si priori model is constructed to restore block sparse signals by Bayesian learning. In this paper, a hierarchical Gao Si priori model based on structural pairing is used to characterize the statistical correlation between signal coefficients under the condition that the noise variance is known, and a set of hyperparametric parameters are used to control the sparsity of the signal. In the traditional Bayesian learning method, each superparameter controls the properties of the corresponding signal coefficients separately. Different from the traditional Bayesian sparse learning method, the prior distribution of each signal sparse is not only related to its own hyperparameter, but also to the prior distribution of each signal in the proposed algorithm based on structural pairings. Moreover, this parameterized model based on structural pairing can correlate the adjacent coefficients with the superparameters of the adjacent coefficients. Therefore, this structure can effectively promote the block clustering features of signals and mine the block priori of signals. In this Gao Si priori model, the expected maximization algorithm is used to recover the block signal by cyclic iteration. At the same time, this paper also considers the signal recovery when the noise variance is unknown. In this case, the signal is regarded as a hidden parameter, and the expected maximization method is used to iterate out the estimated signal and noise variance in turn. In order to achieve sparse signal recovery. An improved reweighted optimization algorithm based on structural pairing is also introduced in this paper. This algorithm can also mine the inner block clustering information of the signal under the premise of unknown signal block structure and sparse degree, and make use of less measurement quantity. An effective recovery signal. In this paper, the restoration of time-varying sparse signals is further studied, that is, the case of multi-slot measurement vector is not considered only in the case of single slot sparse signal recovery. However, unlike the traditional multi-measurement vector, the sparse structure of the multi-measurement signal considered in this paper is no longer constant with time, because in many cases, the position of the non-zero coefficient of the sparse signal changes slowly with time. In this paper, we study the signal recovery problem under this model. The main method is to transform the time-varying sparse signal model into the block sparse signal recovery problem with unknown block structure by mathematical transformation. The simulation results show that the block sparse signals can be recovered effectively by mining the sparse signals and block features, and using the hierarchical Gao Si model based on structural pairing, when the noise variance is known. The signal can be fully recovered with a high probability. When there is noise and the variance of noise is unknown, the signal can be recovered effectively. The simulation of natural data, such as images and sound data, also shows that many signals in nature have such block sparse features, and can be effectively restored by using the algorithm proposed in this paper. On the other hand, the recovery of time-varying signals in DoA model also shows that the proposed algorithm has a good effect on the recovery of time-varying signals.
【学位授予单位】：电子科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN911.7
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本文编号：1964438