兰州大学机构库 >数学与统计学院
基于压缩感知的块稀疏贝叶斯算法在信号处理中的应用
Alternative TitleThe application of BSBL framework based on compressed sensing in signal processing
曹圣明
Thesis Advisor袁敏
2015-05-25
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name学士
Keyword稀疏信号 贝叶斯学习 压缩感知 稀疏i信号恢复
Abstract压缩感知的出现带来了信号处理领域的一场革新,其打破了传统的奈贵斯特采样定理对采样频率的限制,使得我们在进行数据采集的时候,可以在远低于上述采样频率的条件下,实现对原信号的恢复。而稀疏贝叶斯学习最初作为一种机器学习的算法,后来也被应用到稀疏信号的压缩感知领域。贝叶斯学习采用参数化的高斯分布作为解的先验分布,使得它能在无噪、感知矩阵的列间相关性很强、对稀疏解的结构加以利用时,表现出更好的性能,更容易获得最稀疏的解。本文主要研究块状稀疏信号的恢复问题,这种稀疏信号的非零系数在矩阵中呈现块状分布,且其中非零块的位置和大小未知,通过贝叶斯学习的方法,构建高斯先验模型,来恢复块状稀疏信号。针对块状稀疏信号的恢复,本文阐述了三种基本的方法,分别是最大期望值法、边界优化法和定点分析法。并利用这些算法进行了一维脑电信号的恢复,探究了块内联系对恢复效果的影响。并且还用贝叶斯学习算法对图像进行恢复,探究了采样率对恢复效果的影响。BSBL算法以其优良的性能,在信号处理相关领域的应用也越来越广泛。
Other AbstractThe emergence of compressed sensing brings an innovation in the field of signal processing, which breaks the limit on the sampling frequency in the traditional Nyquist sampling theorem.So that when we conduct the data collection, we can make the sampling frequency relatively lower far below the Nyquist's to achieve the recovery of the original signal.The sparse Bayesian learning (SBL), initially known as a kind of machine learning algorithm, is also applied to the field of compressed sensing of sparse signals. SBL has many significant advantages and flexibility. The flexibility comes from the truth that SBL uses parameterized Gaussian distribution as prior distribution, so that it can work well in noisy environment, when the correlation between the columns of the sensing matrix is accounted,and when we need to take advantage of the structure of the sparse signal. Relatively, SBL shows better performance and make it an easier access to get the most sparse solution.This paper majors in the recovery of the block-sparse signals. The non-zero coefficients of sparse signal lie in the matrix as blocks. The position and size of the non-zero blocks remains undermined. With respect to Bayesian learning method, we construct a prior Gaussian model to restore the block sparse signal. For recovery of block sparse signal, the paper describes three basic methods, namely expectation-maximization (EM), boundary-optimization (BO) and fix-point analysis. We use these algorithms to restore the one-dimensional Electroencephalogram (EEG) signals and explore the influence of block incoherence to the recovery efficiency.We also explore if the sampling rate will make an effect to the recovery performance. BSBL algorithm, due to its excellent performance, will be increasingly popular in the field of signal processing.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/225093
Collection数学与统计学院
Recommended Citation
GB/T 7714
曹圣明. 基于压缩感知的块稀疏贝叶斯算法在信号处理中的应用[D]. 兰州. 兰州大学,2015.
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