压缩感知低密度奇偶观测矩阵的构造与应用研究

发布时间：2018-03-04 07:10

本文选题：压缩感知　切入点：观测矩阵　出处：《南京理工大学》2017年硕士论文　论文类型：学位论文

【摘要】：压缩感知理论解决了传统采样理论对带宽要求的瓶颈,以"边采样边压缩"的方式直接对信号进行处理,其中采样中最关键的环节就是观测矩阵的构造。性能优良的观测矩阵将信号投影到低维空间,得到的观测值包含尽可能多的原始信号的重要信息,这样确保更精准地重构出原始信号。本文围绕观测矩阵的构造问题,深入研究了观测矩阵的分类以及各类观测矩阵的构造原理和方法。针对现有的常用观测矩阵存在的问题,本文提出了相应的构造和改进方法,主要的创新工作包括:(1)针对现有观测矩阵构造复杂且元素不是二值化的问题,在已有的低密度奇偶观测矩阵基础上,提出一种级联LDPC观测矩阵的构造方法。LDPC校验矩阵的构造条件之一就是各列元素之间保持不相干性,满足观测矩阵的RIP准则,故将其应用于压缩感知中作为观测矩阵使用。级联LDPC观测矩阵的构造受Mackay 1A构造法的启发,用Gallager构造法取代Mackay构造法中部分内容,由这两者级联生成。实验结果表明,级联LDPC观测矩阵性能优于用单一方法构造的LDPC观测矩阵。(2)针对现有观测矩阵存储量大且不易于硬件实现的问题,在LDPC观测矩阵的基础上,提出对角化LDPC观测矩阵的构造方法。将LDPC观测矩阵与对角块矩阵相结合,生成对角化LDPC观测矩阵。对角线位置放置相同的LDPC块,不仅简化构造复杂度,而且能够减小存储空间,只需要存储一个LDPC块大小的元素,即可得到一个完整的对角化LDPC观测矩阵。实验结果表明,对角化LDPC观测矩阵具有以下优势:a.构造简单且矩阵元素少;b.重构精度高;c.计算量和存储空间小;d.方便硬件实现。将对角化LDPC观测矩阵应用于遥感图像重构仿真实验,重构效果优于其他观测矩阵,且重构时间较短。(3)针对图像数据采样的复杂性,同时为了验证观测矩阵的性能,本文设计实现一个压缩感知图像重构仿真软件系统。该软件能够清晰地看到压缩感知图像重构的所有流程,包括图像信号的稀疏表示、信号的感知采样和图像信号的重构。软件侧重于观测矩阵的采样过程,可以根据需求生成所需大小的观测矩阵,并且直观地看到观测矩阵的图像,便于更形象地了解观测矩阵。重构后能够看到重构图像以及图像重构的评价指标PSNR 和 SSIM 值。
[Abstract]:Compression sensing theory solves the bottleneck of bandwidth requirement in traditional sampling theory, and directly processes the signal in the way of "edge sampling and compression". The construction of observation matrix is the most important part in sampling. The observation matrix with good performance projects the signal into low dimensional space, and the obtained observation value contains as much important information as possible of the original signal. In this paper, the classification of observation matrix and the construction principle and method of all kinds of observation matrix are studied. In this paper, the corresponding construction and improvement methods are proposed. The main innovation work includes: 1) aiming at the problem of complex construction and non-binarization of the existing observation matrix, based on the existing low density odd-even observation matrix, This paper presents a method of constructing cascaded LDPC observation matrix. One of the conditions of constructing the check matrix is that the elements of each column remain incoherent, which satisfies the RIP criterion of the observation matrix. Therefore, it is applied to compressed perception as observation matrix. The construction of cascaded LDPC observation matrix is inspired by Mackay 1A construction method, and some contents of Mackay construction method are replaced by Gallager construction method, which are generated by these two cascading methods. The experimental results show that, The performance of cascaded LDPC observation matrix is better than that of LDPC observation matrix constructed by single method. Aiming at the problem that the existing observation matrix has large storage capacity and is difficult to be implemented in hardware, the performance of cascade LDPC observation matrix is better than that of LDPC observation matrix constructed by a single method. A method of constructing diagonal LDPC observation matrix is presented. The diagonal LDPC observation matrix is generated by combining the LDPC observation matrix with diagonal block matrix. The diagonal position of the same LDPC block not only simplifies the construction complexity, but also reduces the storage space. A complete diagonal LDPC observation matrix can be obtained by simply storing an element of LDPC block size. The experimental results show that, The diagonal LDPC observation matrix has the following advantages: A. simple construction, few matrix elements, high reconstruction precision, small computation and storage space, convenient hardware realization. The diagonal LDPC observation matrix is applied to remote sensing image reconstruction simulation experiment. The reconstruction effect is better than other observation matrices, and the reconstruction time is shorter. In this paper, we design and implement a compressing perceptual image reconstruction simulation software system, which can clearly see all the processes of compressed perceptual image reconstruction, including sparse representation of image signals. The software focuses on the sampling process of the observation matrix, and can generate the observation matrix of the required size according to the requirement, and can see the image of the observation matrix intuitively. It is convenient to understand the observation matrix more vividly. After reconstruction, we can see the reconstructed image and the evaluation index PSNR and SSIM value of image reconstruction.
【学位授予单位】：南京理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP391.41

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