基于样本与多项式核表示的非线性稀疏信号重构研究

发布时间：2018-03-10 12:37

本文选题：压缩感知　切入点：样本非线性压缩感知　出处：《西南大学》2017年硕士论文　论文类型：学位论文

【摘要】：压缩感知的有效性以信号的稀疏性为前提.目前已知的信号稀疏性是指存在某个线性变换使信号在该变换下稀疏.然而,随着压缩感知研究的持续深入,这种基于线性表示的稀疏结构越来越不能满足日益增长的理论和应用需求.为了应对这一挑战,本文提出了基于样本的经由非线性变换刻画稀疏性的新模型.不同于现有基于核主成分分析和K-SVD的非线性稀疏表示模型,我们提出的模型充分借助于样本数据信息,很好地实现了复杂(非线性)信号的鲁棒重构.全文结构以及得到的结论如下:第一章为引言,介绍了传统压缩感知和非线性稀疏信号重构即非线性压缩感知的研究背景及其研究现状,并给出了全文的组织结构和主要内容安排.第二章对压缩感知中应用于稀疏信号恢复的重构理论进行了简要的叙述,其中主要包含几个主要研究的方向,分别为信号稀疏表示、测量矩阵设计和重构算法设计.其中就信号稀疏表示部分还对现在非线性压缩感知初步的研究进行了简要的介绍,即非线性信号的稀疏表示初步研究.第三章针对现有基于线性表示的稀疏结构的不足给出了非线性压缩感知对于非线性信号的的两个假设并给出了核传感矩阵的定义.并根据计算得出了非线性信号在核函数条件下经核压缩矩阵在得到稀疏向量β的估计值?β的条件下间接求解原始非线性稀疏信号.根据传统压缩传感中关于MIP,RIP的定义,给出了相应的非线性压缩传感理论意义上的KMIP,KRIP的定义,并在定义的条件下研究了非线性压缩传感模型(3.4)的求解问题,得到了该问题鲁棒重构的充分条件,因此我们最终能间接得到原始非线性稀疏信号精确重构.第四章针对第三章提出新的算法SNCS,首先对不同的参数c和d对数据“Sculpture Face”选取其中一幅图片进行恢复对比均方误差和相干性KMIP确定最终参数的选择为c=30,d=3,并与现有的KTCS、KCS算法以及传统的?1最小化算法恢复效果作比较.实验结果标明:在合适的选择测量矩阵A和样本集X以及核函数κ(x,y)=fk(?x,y?)的条件下,样本非线性压缩传感算法(SNCS)具有理想的重构效果,该结果还表明在低测量数的条件下算法依旧对非线性稀疏信号有优于传统压缩传感的重构效果.第五章针对行文做的工作进行了归纳和总结,并对可以作为后续研究的方向做出了分析及展望.
[Abstract]:The effectiveness of compression sensing is premised on the sparsity of signal. At present, the known signal sparsity refers to the existence of a linear transformation to make the signal sparse under the transformation. However, as the research of compression perception continues to deepen, This linear representation based sparse structure is increasingly unable to meet the growing theoretical and application needs. In this paper, a new model based on samples to characterize sparsity by nonlinear transformation is proposed. Different from the existing nonlinear sparse representation models based on kernel principal component analysis and K-SVD, the proposed model is based on the information of sample data. The robust reconstruction of complex (nonlinear) signals is well realized. The structure of the paper and the conclusions obtained are as follows: chapter 1 is the introduction. This paper introduces the research background and present situation of traditional compression sensing and nonlinear sparse signal reconstruction, that is, nonlinear compression sensing. In chapter 2, the reconstruction theory applied to sparse signal recovery in compressed sensing is briefly described, which includes several main research directions, namely, sparse signal representation. Measurement matrix design and reconstruction algorithm design. In the signal sparse representation part, the preliminary research on nonlinear compression perception is also briefly introduced. In chapter 3, we give two hypotheses of nonlinear compression sensing for nonlinear signals, and give the kernel sensing matrix for the sparse structure based on linear representation in order to solve the problem of sparse representation of nonlinear signals. Definition. According to the calculation, we get the estimate of sparse vector 尾 by kernel contraction matrix under the condition of kernel function. Under the condition of 尾, the original nonlinear sparse signal is indirectly solved. According to the definition of MIPN RIP in traditional compression sensing, the definition of KMIP / KRIP in the sense of nonlinear compression sensing theory is given. The problem of nonlinear compression sensing model (3.4) is studied under the defined conditions, and the sufficient conditions for robust reconstruction of the problem are obtained. In Chapter 4th, a new algorithm is proposed for the third chapter, in which the different parameters c and d are used to select one of the images of the data "Sculpture Face". Mean square error (MSE) and coherence (KMIP) determine the choice of final parameters as C ~ (30) / D ~ (3), and compared with the existing KTCSN KCS algorithm and the traditional KCS algorithm. The experimental results show that the measurement matrix A and the sample set X and the kernel function 魏 X are selected properly. X,y? The sample nonlinear compression sensing algorithm (SNCSs) has an ideal reconstruction effect. The results also show that the algorithm is better than the traditional compression sensor in the reconstruction of nonlinear sparse signals under the condition of low measurements. Chapter 5th summarizes and summarizes the work done in the paper. It also makes an analysis and prospect for the future research.
【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN911.7

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