基于信号稀疏表示的重构与分类算法研究

发布时间：2018-04-21 00:18

本文选题：稀疏表示 + 匹配追踪　；参考：《西安电子科技大学》2014年硕士论文

【摘要】：作为压缩感知理论的研究核心之一，对冗余字典下信号稀疏表示理论的研究越来越受到人们的重视，该方法的核心是为了在变换域上，利用尽可能少的原子的线性组合来逼近原始信号，通过得到为数不多的非零信息来揭示信号的本质特性，从而使对信号的处理变得高效而又简单。本文基于稀疏表示的相关理论，重点研究了基于匹配追踪思想的信号重构与分类算法。基于稀疏表示的图像重构中，介绍了经典的匹配追踪类算法，详细地分述了各算法的思路、流程及特点，并针对原有的SAMP算法存在的两点缺陷，即初始迭代步长难以确定和耗时较多的问题进行改进，提出了稀疏度自适应贪婪(SAGP)算法。通过一维稀疏信号和二维真实图像的重构实验，验证了SAGP算法重构效果优于SAMP算法的同时，也保持了时间的优越性。基于稀疏表示的分类中，针对CSSOMP算法中异类原子集间存在交集的问题，进一步优化了MCSSOMP算法，并增加了大量实验。MCSSOMP算法采用约束原子集间相互独立的策略，能够减少异类信号间的共性因素，强化信号间的区分度。标准图像库和实测雷达信号集上的大量实验，从多个角度验证了改善后的算法在提升分类效果方面具有良好的表现，，特别是在噪声和遮挡较为严重情况下，仍有较强的鲁棒性。基于字典更新思想的分类中，针对LC-KSVD算法在字典初始化时过于侧重局部信息，而非从全局考虑的问题，提出了MLC-KSVD算法。该方法在初始化时采用分类SOMP算法的策略，即每类信号挑选共同的原子集，而异类信号选取不同的原子集，使改进后的算法能更适于分类识别。各种图像数据库和实测雷达数据集上的实验，证实了所提算法在多种信号分类识别中的有效性。
[Abstract]:As one of the core of compressed sensing theory, the research on sparse representation theory of signals in redundant dictionaries has been paid more and more attention. The core of this method is in the transform domain. The linear combination of as few atoms as possible is used to approximate the original signal, and the essential characteristics of the signal are revealed by obtaining a few non-zero information, which makes the signal processing more efficient and simple. Based on the theory of sparse representation, this paper focuses on the algorithm of signal reconstruction and classification based on the idea of matching and tracking. In image reconstruction based on sparse representation, the classical matching and tracing algorithms are introduced, the ideas, flow and characteristics of each algorithm are described in detail, and the two defects of the original SAMP algorithm are pointed out. That is, the initial iteration step size is difficult to determine and time-consuming to improve, a sparse adaptive greedy SAGP-based algorithm is proposed. Through the experiments of one dimensional sparse signal and two dimensional real image reconstruction, it is proved that the reconstruction effect of SAGP algorithm is better than that of SAMP algorithm, while maintaining the superiority of time. In the classification based on sparse representation, aiming at the problem of intersecting among different atomic sets in CSSOMP algorithm, this paper further optimizes the MCSSOMP algorithm, and adds a lot of experiments. MCSSOMP algorithm adopts the strategy of independent between constrained atomic sets. It can reduce the common factors among heterogeneous signals and strengthen the differentiation between signals. A large number of experiments on the standard image database and the measured radar signal set show that the improved algorithm has a good performance in improving the classification performance from several angles, especially in the case of serious noise and occlusion, there is still strong robustness. In the classification based on the idea of dictionary updating, the MLC-KSVD algorithm is proposed to solve the problem that the LC-KSVD algorithm emphasizes the local information rather than the global consideration when initializing the dictionary. In this method, the strategy of classifying SOMP algorithm is adopted in initialization, that is, each kind of signal selects a common atomic set, while a different class signal selects different atomic sets, which makes the improved algorithm more suitable for classification and recognition. Experiments on various image databases and measured radar datasets show that the proposed algorithm is effective in the classification and recognition of various signals.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN911.7

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