基于能量的稀疏重建及多尺度压缩感知的研究

发布时间：2018-06-27 23:51

本文选题：压缩感知 + 贪婪算法　；参考：《西南交通大学》2014年博士论文

【摘要】：面对人类对数据需求的日益增长,以香农—奈奎斯特采样定理为基础的信号处理框架,不可避免给信息系统的信号处理能力与硬件实现带来了极大的挑战。近年来,一种新的利用信号的稀疏或可压缩的先验特性的信号采集和压缩理论——压缩感知理论被提出,并受到了学术界和工业界的广泛关注。在压缩感知框架下,使用远低于传统的奈奎斯特采样频率的速率去采样先验稀疏或可压缩的信号,其最大的特点是采样与压缩同步进行,因此能够有效降低数据的传输量和存贮量。压缩感知理论的研究涉及到信号的稀疏重建算法、稀疏表示以及观测矩阵的设计。信号的稀疏重建算法主要实现对信号快速准确的重建。稀疏表示的目标是寻找一个合适的基,在此基下信号能够使用少量的系数来揭示有用的信息。观测矩阵的设计涉及约束等距性质、非相干特性等要求。本文以压缩感知为核心,重点围绕盲稀疏度下信号的重建,以及压缩感知与轮廓波的结合等问题进行研究,主要贡献和创新工作如下：(1)可变步长分阶段自适应匹配追踪算法考虑到恢复未知信号时,其稀疏度不能提前知晓这个实际问题,对盲稀疏度下信号的重建进行研究,系统总结了匹配追踪类算法,深入分析了具有回溯思想的匹配追踪类算法。针对自适应匹配追踪算法用于重建二维图像时对步长敏感的问题,提出了可变步长的分阶段自适应匹配追踪算法。根据四比一法则,通过控制因子控制当前迭代所估计的信号稀疏度。若当前迭代所得到的信号尺寸较小时,使用可变的大步长；若当前迭代估计到的信号尺寸较大时,使用不变的步长。随着迭代的进行,稀疏度将逐步逼近真实值。实验仿真表明,该方法不仅克服了步长对重建质量的影响,而且提高了图像的峰值信噪比。(2)基于能量的固定步长的自适应匹配追踪算法针对匹配追踪算法对二进制稀疏信号成功重建率较低的问题,从数学角度证明了观测值和原始信号之间能量的关系,在此基础上提出基于能量的固定步长的自适应匹配追踪算法。通过将观测值的能量引入到信号重建过程中,并根据观测值和候选信号能量之间的关系判断是否使用步长去增加当前估计到的稀疏度,以达到通过迭代实现估计的稀疏度逐步逼近真实值的目的。通过实验仿真验证了该算法对二进制稀疏信号具有较高的成功重建率,较少的重建时间以及迭代次数。(3)基于能量的可变步长的白适应匹配追踪算法为了提高基于能量的固定步长匹配追踪算法的自适应性,提出可变步长的能量自适应匹配追踪算法。根据当前的候选信号与观测值能量之间的关系,将重建过程分为三个阶段,通过两者之间能量的大小自主选择每次迭代所采用的步长。实验仿真表明该算法在成功重建的频率,重建时间以及迭代次数方面均优于其他相比较的追踪类算法,并从数学角度证明了步长与稀疏度之间的关系以及重建阶段的完整性和有序性。该算法的提出进一步扩大了匹配追踪算法的应用范围。(4)基于小波变换的轮廓波域多尺度压缩感知方案针对使用传统的压缩感知模型采样二维信号时,所需大尺寸观测矩阵和较大传输量的问题,提出将属于多尺度几何分析的轮廓波与压缩感知相结合,设计了基于小波变换的轮廓波域多尺度压缩感知方案。该方案将小波变换引入到轮廓波域,即对轮廓波域的方向子带使用小波变换进行压缩。该变换使得所需观测的系数的维度进一步减少,所需观测矩阵的尺寸也必然减小,以达到降低传输量和计算存储的开销,提高图像重建质量的目的。通过与基于曲线波的多尺度压缩感知相比较,仿真结果表明：该算法不仅降低了传输量,而且在重建质量和所需矩阵的尺寸方面都有较大的改进。通过将本文所提出的算法与基于小波变换的多尺度压缩感知进行比较,验证了本文算法的有效性,并通过实验给出了本文算法的动机。(5)基于非下采样轮廓波的含噪图像CS重建算法考虑到非下采样轮廓波能够有效去除图像的噪声,在压缩感知框架下提出基于非下采样轮廓波域的含噪图像重建算法。通过使用光滑投影兰德韦伯(SPL)算法重建图像的同时,在非下采样轮廓波域使用门限操作去除噪声。在此基础上引入非局部均值滤波对重建后的图像进行滤波处理。仿真结果表明,该算法比基于轮廓波域的SPL算法具有更好的重建效果和去噪能力。
[Abstract]:In the face of the growing demand for data, the signal processing framework based on Shannon Nyquist sampling theorem inevitably brings great challenges to the signal processing capability and hardware implementation of the information system. In recent years, a new theory of signal acquisition and compression using sparse or compressible prior characteristics of signals is proposed. Compression perception theory has been proposed and received extensive attention from academia and industry. Under the framework of compressed sensing, the prior sparse or compressible signals are sampled at a much lower rate than the traditional Nyquist sampling rate. The greatest feature is that sampling and compression are carried out in the same step, and thus the transmission of data can be effectively reduced. The research of compressed sensing theory involves sparse reconstruction of signals, sparse representation and the design of observation matrices. The sparse reconstruction algorithm of the signal mainly realizes the rapid and accurate reconstruction of the signal. The target of the sparse representation is to find a suitable base. Under this basis, the signal can use a small number of coefficients to reveal the usefulness. Information. The design of the observation matrix involves constraint equidistance properties, non coherent characteristics and so on. This paper focuses on compressed sensing as the core, focusing on the reconstruction of signals under blind sparsity, and the combination of compressed sensing and contour waves. The main contributions and innovations are as follows: (1) variable step size adaptive matching tracking algorithm Considering that the unknown signal is restored, the sparsity of the method can not be known in advance, and the reconstruction of the signal under blind sparsity is studied. The matching pursuit class algorithm is summarized, and the matching tracking algorithm with backtracking is deeply analyzed. The adaptive matching tracking algorithm is sensitive to the step size for the reconstruction of the two-dimensional image. A phased adaptive matching tracking algorithm with variable step size is proposed. According to the four to one rule, the signal sparsity estimated by the current iteration is controlled by the control factor. If the signal size obtained by the current iteration is smaller, a variable large step is used; if the current iteration is estimated to be larger, the invariant is used. Step size. With the iteration, the sparsity will gradually approach the real value. Experimental simulation shows that the method not only overcomes the effect of the step size on the reconstruction quality, but also improves the peak signal to noise ratio of the image. (2) the adaptive matching tracking algorithm based on the fixed step length based on energy is successfully reconstructed for the binary sparse signal. The relationship between the observed value and the energy of the original signal is proved mathematically. On this basis, an adaptive matching tracking algorithm based on the energy based fixed step length is proposed. By introducing the energy of the observed value into the process of the signal reconstruction, and judging whether it is used according to the relationship between the observed value and the energy of the candidate signal. The step length increases the sparsity of the estimated current to achieve the goal of gradual approximation of the true value by iterative realization of the estimated sparsity. The experimental simulation shows that the algorithm has a high successful reconstruction rate for binary sparse signals, less reconstruction time and iteration times. (3) the white adaptation matching based on the variable step size of energy. In order to improve the adaptability of the fixed step matching tracking algorithm based on energy, the tracking algorithm proposes a variable step size adaptive matching tracking algorithm. According to the relationship between the current candidate signal and the observation energy, the reconstruction process is divided into three stages, and each iteration is selected independently by the size of the energy between the two. The experimental simulation shows that the algorithm is better than the other tracking algorithms in the frequency of successful reconstruction, the time of reconstruction and the number of iterations. The relationship between the step length and the sparsity and the integrity and order of the reconstruction phase are proved from the mathematical point of view. The proposed algorithm further expands the matching tracking algorithm. The application scope of the method. (4) the multiscale compression perception scheme based on the wavelet transform based contours domain is designed to solve the problem of large size observation matrix and large transmission amount when using the traditional compressed sensing model to sample the two-dimensional signal. This scheme introduces the wavelet transform into the contour domain, that is, the wavelet transform is used to compress the direction subband of the contour wave domain. This transform makes the dimensions of the measured coefficients further reduced, and the size of the observed matrix is also reduced, in order to reduce the amount of transmission and calculate storage. By comparing with the multiscale compression based on curve wave, the simulation results show that the algorithm not only reduces the amount of transmission, but also improves the quality of reconstruction and the size of the required matrix. By the algorithm proposed in this paper and the multiscale compression based on the wavelet transform The effectiveness of this algorithm is verified by comparison, and the motivation of this algorithm is given through experiments. (5) the CS reconstruction algorithm based on non down sampled contours is considered to be able to effectively remove the noise of the image by non down sampling contour waves, and proposes a noisy image based on the non down sampling contour domain under the compressed sensing framework. Reconstruction algorithm. By using the smooth projection lander Weber (SPL) algorithm to reconstruct the image, the threshold operation is used to remove the noise in the non lower sampling contour domain. On this basis, the non local mean filter is used to filter the reconstructed image. The simulation results show that the algorithm is better than the SPL algorithm based on the contour domain. Reconstruction effect and de-noising ability.
【学位授予单位】：西南交通大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TN911.7

【参考文献】