压缩感知的测量矩阵与图像融合应用研究

发布时间：2018-01-08 13:22

本文关键词：压缩感知的测量矩阵与图像融合应用研究　出处：《中国科学技术大学》2016年硕士论文　论文类型：学位论文

【摘要】：压缩感知理论能够充分利用信号稀疏的特性,通过投影矩阵将高维的信号投影到低维数据空间中。该理论相比奈奎斯特采样能够减少采样数据量,节省宝贵的存储空间和紧张的宽带资源,后期通过压缩感知重构算法从少量的采样数据中恢复出原信号,这个采样过程将传统的数据采样与压缩合二为一,能够降低采样数据的获取时间和存取空间。所以压缩感知一经提出,就得到许多学者的高度关注,成为近年来非常热门的研究领域,在雷达信号、遥感图像、医学图像、无线网络等领域得到应用和发展,有着非常广泛的应用前景。设计一个结构简单、性能优越、便于研究控制的测量矩阵,是压缩感知理论研究中重要的部分,也是压缩感知在应用中的前提保证。压缩感知成像系统获得的仅是原始信号的投影测量值,依赖于观测矩阵的选择,压缩图像融合是对测量值的融合,如何选择融合参数是一个需要解决的问题。而测量值包含的信息越多,效果越好,因此构造合适的测量矩阵是融合成功的保证。本文的研究成果如下：(1)构造确定性结构的傅里叶观测矩阵部分傅里叶测量矩阵能够应用快速傅里叶方法,可以大大提高计算速度,降低运算量,且恢复效果好,但是随机部分傅里叶测量矩阵与其他随机测量矩阵都有相似的问题,其复杂性使得存储和硬件实现不方便。A.Devore提出的确定性测量矩阵,其确定性使得测量矩阵可控制强,存储和实现较方便,但其恢复效果一般。我们的思路是结合确定性测量矩阵和部分傅里叶测量矩阵的优点,构造一种确定性结构的傅里叶测量矩阵。这种测量矩阵的选择不再是随机性的,而是可控制的,其复杂度较低,易于控制实现。利用反馈移位寄存器(Linear Feedback Shift Register,LFSR),我们构造一个伪随机整数产生算法,生成我们需要的索引集,通过傅里叶矩阵来构造我们想要的确定性测量矩阵。利用Gersgorin圆盘定理和Weyl级数定理,理论上可以证明我们构造的确定性测量矩阵是满足RIP条件和MIP条件。通过一维信号和二维图像仿真实验,与常用的高斯测量矩阵、部分哈达玛测量矩阵等比较,在相同观测量M和相同稀疏度K下,恢复成功率更高；在均方根误差(RMSE)、峰值信噪比(PSNR)和结构相似度(SSIM)信号处理衡量指标中取得优势,说明信号恢复质量较好。(2)研究压缩感知观测量特征并应用到压缩图像融合基于压缩感知的图像融合,利用尽量少的数据提取尽量多的信息,可以极大地提高数据传输与存储的效率,减少计算复杂度,是一种简便而高效的融合手段。压缩感知成像系统获得的仅是原始信号的投影测量值,依赖于测量矩阵的选择。通过对观测量特性的研究,数据分析压缩感知观测量与原图像特征信息之间的关联性,将其作为融合参数的选取的依据。进而提出一种利用观测量特征,采用粒子群优化算法选取融合参数的压缩感知图像融合方法。实验仿真,对比单目标优化目标函数和多目标优化函数选取融合参数方法,通过客观的评价指标进行融合质量评价,提出的方法融合效果在一些评价指标中具有优势。
[Abstract]:To make full use of the sparse characteristics of compressed sensing theory, the signal is projected through the projection matrix will be high-dimensional to low dimensional data space. This theory than Nyquist sampling can reduce the amount of sampling data, saving valuable storage space and the shortage of broadband resources, later through compressed sensing reconstruction algorithm to recover the original signal from small sample data in the sampling process of traditional data sampling and compression can reduce the sampling data be made one, access time and access space. So the compressed sensing was put forward, get the attention of many scholars, become a very hot research field in recent years, in the radar signal, remote sensing image, medical image, application and development the wireless network and other fields, has a very broad application prospects. The design of a simple structure, superior performance, easy control of measurement matrix is pressure An important part of shrinkage perception theory, is the premise in the application of compressed sensing. Compressed sensing imaging system for measurement of projection of the original signal is only dependent on the value of the observation matrix, compressed image fusion is the fusion of the measured value, how to choose the combination of parameters is a problem to be solved. The measured value of the information contained in the more, better, so the measurement matrix is suitable for integration to ensure the success of the research achievements of this paper are as follows: (1) Fu Liye Fu Liye measurement matrix observation matrix to construct deterministic structure can be used for fast Fu Liye method, can greatly improve the calculation speed, reduce the amount of computation and good recovery effect however, part of the Fu Liye random measurement matrix and other random measurement matrix has a similar problem, the complexity of hardware implementation is not convenient to store and put forward by.A.Devore The deterministic measurement matrix, the uncertainty of the measurement matrix can control, storage and the implementation is convenient, but the recovery effect in general. The idea is that by combining the advantages of deterministic measurement matrix and partial Fourier measurement matrix, Fourier measurement matrix to construct a deterministic structure. The measurement matrix is no longer a choice of random, but can control, which has low complexity and is easy to control. The use of feedback shift register (Linear Feedback Shift Register, LFSR), we construct a pseudo random integer generation algorithm, we need to construct the index set of measurement matrix to determine what we want by Fourier matrix. By using the Gersgorin disc theorem and Weyl series theorem can be proved theoretically determined we construct the measurement matrix is satisfying RIP condition and MIP condition. Through one-dimensional signal and two-dimensional image simulation, Gauss and the measurement matrix is used, comparison of Hadamard measurement matrix, in view of the same measurement of M and K under the same sparsity recovery, higher success rate; the root mean square error (RMSE), the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) to take advantage of the signal processing measure, indicating the signal the restoration quality is good. (2) research on compressed sensing measurements and is applied to the compression of image fusion image fusion based on compressed sensing, try to use less data to extract as much information as possible, can greatly improve the efficiency of data transmission and storage, reduce the computational complexity, is a simple and efficient means of fusion compression. Sensing imaging system to obtain the projection of the original signal is only the measurement value depends on the measurement matrix. Through the research on the concept of measurement characteristics, data analysis on relationship between compressed sensing measurement and image feature information, As the fusion parameters selection basis. Then put forward a concept of using measurement features, using particle swarm optimization algorithm to select the compressed sensing image fusion method. The parameters of experimental simulation, single objective optimization function and multi-objective function optimization parameters selection of fusion method contrast, fusion quality evaluation by objective evaluation index, put forward the method has some advantages in the fusion effect evaluation index.

【学位授予单位】：中国科学技术大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TN911.7

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