块稀疏信号重构算法研究

发布时间：2018-06-12 03:27

本文选题：块稀疏信号重构 + 未知块结构　；参考：《电子科技大学》2017年硕士论文

【摘要】：稀疏重构作为压缩感知中的一个重要研究课题,其主要研究内容是如何在保证信号重构精度的前提下用低维的测量量来恢复高维稀疏信号。传统的稀疏表示理论假定稀疏信号中的非零元素都是随机分布在信号中,但是在处理实际问题时,稀疏信号中的非零元素往往具有一定的结构特性,充分利用信号内非零元素之间的结构特性可以建立更准确的重构信号模型,势必会提高重构算法的性能,具有重要的研究意义。本文针对具有分块结构的稀疏信号重构问题进行研究。首先针对已知块结构的重构问题,对基于贪婪迭代的块稀疏重构算法和稀疏块自适应迭代算法进行研究,然后针对实际应用中常出现的未知块结构的重构问题,研究了块稀疏贝叶斯算法和结构耦合稀疏贝叶斯算法。通过对结构耦合稀疏贝叶斯(Pattern Coupled Sparse Bayesian learning,PCSBL)算法的研究分析,发现PCSBL算法将控制元素稀疏性的超参数互相关联,使用一个预先设置好的参数来控制信号元素受相邻元素的影响程度。然而,在实际的块稀疏信号中,相邻超参数之间的相关性并非处处相同。本文针对结构耦合稀疏贝叶斯算法的不足之处进行了改进,提出了能够将信号相邻元素的稀疏度以自适应方式联系起来的稀疏块自适应耦合算法。本文提出的新算法用一组能够自适应求解的耦合参数代替结构耦合稀疏贝叶斯算法中的单一预定参数去表示相邻超参数之间的相关性。稀疏块自适应耦合算法将互相独立的超参数经过线性变换得到新的相关超参数,建立了一个新的分层高斯先验模型。实验证明,与目前已有的块稀疏重构算法相比,本文提出的使用自适应耦合参数的稀疏贝叶斯算法能够获得更好的块稀疏重构性能。为了防止稀疏块自适应耦合算法存在过拟合问题,本文还对新算法的分层模型进行简化,使耦合参数与超参数一一对应,并提出了一种简化的稀疏块自适应耦合算法。简化模型和算法不仅能够降低计算量,还能够在一定程度上避免过拟合问题的出现。
[Abstract]:Sparse reconstruction is an important research topic in compression sensing. Its main research content is how to restore high-dimensional sparse signals with low-dimensional measurements while ensuring the precision of signal reconstruction. The traditional sparse representation theory assumes that the non-zero elements in sparse signals are randomly distributed in the signals, but when dealing with practical problems, the non-zero elements in sparse signals often have certain structural characteristics. A more accurate reconstruction signal model can be established by making full use of the structural characteristics of non-zero elements in the signal, which will improve the performance of the reconstruction algorithm and have important research significance. In this paper, the problem of sparse signal reconstruction with block structure is studied. Firstly, for the reconstruction of known block structures, the block sparse reconstruction algorithm based on greedy iteration and the sparse block adaptive iterative algorithm are studied. Block sparse Bayes algorithm and structurally coupled sparse Bayesian algorithm are studied. Through the research and analysis of the structure-coupled sparse Bayesian Bayesian learning PCSBL algorithm, it is found that the PCSBL algorithm correlates the superparameters controlling the sparsity of the elements, and uses a pre-set parameter to control the influence of the signal elements on the adjacent elements. However, in the actual block sparse signal, the correlation between adjacent superparameters is not the same everywhere. In this paper, we improve the structural coupling sparse Bayes algorithm, and propose a sparse block adaptive coupling algorithm which can relate the sparsity of adjacent elements to the adaptive method. In this paper, a set of coupling parameters can be solved adaptively instead of a single predefined parameter in the structural coupled sparse Bayes algorithm to represent the correlation between adjacent superparameters. The sparse block adaptive coupling algorithm obtains a new correlation hyperparameter by linear transformation of independent superparameters and establishes a new hierarchical Gao Si priori model. Experimental results show that the proposed sparse Bayesian algorithm with adaptive coupling parameters can achieve better block sparse reconstruction performance than the existing block sparse reconstruction algorithms. In order to prevent the over-fitting problem of sparse block adaptive coupling algorithm, this paper also simplifies the layered model of the new algorithm to make the coupling parameters correspond to the superparameters one by one, and proposes a simplified sparse block adaptive coupling algorithm. The simplified model and algorithm can not only reduce the computational complexity, but also avoid the problem of over-fitting to a certain extent.
【学位授予单位】：电子科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN911.7

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