【作者】 曹离然；

【导师】 彭喜元；

【作者基本信息】 哈尔滨工业大学 ， 仪器科学与技术， 2011， 硕士

【摘要】 压缩感知(Compressed Sensing, CS)是近年来信号处理领域最热门的研究方向之一,由于其特殊的采样方式可以突破传统奈奎斯特(Nyquist)定理的限制,因此在雷达成像、无线传感器网络、射频通信、医学图像处理、图像设备采集等方面有非常广阔的应用前景。压缩感知的一个重要任务就是对压缩采样后的信号进行重构,目前引起了众多学者的关注和研究。本文主要从压缩感知基本理论出发,对压缩感知重构算法目前存在的一些问题进行深入研究。从提高信号重构概率、降低复杂度等方面入手,首先对压缩感知标准稀疏信号常用算法进行了总结,尤其针对匹配追踪(Matching Pursuit, MP)类算法进行了详细阐述,然后研究了基于块稀疏信号模型的重构算法,最后研究了面向模拟信息转换(Analog to Information Converter, AIC)的重构算法,并通过仿真实验验证了算法的有效性。本文的主要研究内容和取得的成果如下:1.总结部分常用标准稀疏信号重构算法,并进行对比实验,尤其深入研究匹配追踪类算法,重点针对目前正交匹配追踪(Orthogonal Matching Pursuit, OMP)算法中匹配操作采用内积不准确的缺点,提出了一种基于相关系数的修正OMP算法。该算法利用相关系数代替内积进行原子匹配操作,提高了寻找信号支撑集的概率,从而提高了最后信号的重构概率。仿真实验表明该算法在一维信号的重构概率以及二维图像信号的重构信噪比等方面均优于标准OMP算法,具有较好的适用性。2.研究基于块稀疏模型的信号重构算法,针对大多数块稀疏信号重构算法重构概率低、复杂度高以及所需先验知识多等缺点,提出了三种改进算法。首先引入子空间及回溯思想,提出了一种块稀疏子空间匹配追踪算法。该算法每次迭代对整个信号支撑块进行估计,且利用回溯对上一次估计的信号支撑集进行修正,该算法在复杂度和重构概率方面较多数块稀疏信号重构算法都有提高。然后,本文针对实际中块稀疏度未知的问题,提出了一种块稀疏度自适应迭代重构算法,该算法不需块稀疏度作为先验知识,只需初始化块稀疏度进行迭代,直到估计出块稀疏度和源信号为止。该算法在复杂度方面和原有多数重构算法具有相同的数量级,但重构概率有了提高。最后,本文针对实际中块稀疏度和块大小都未知的情况,提出了分块大小未知的自适应匹配追踪算法,该算法不需要块大小以及块稀疏度的先验知识,只需初始化块大小和块稀疏度,迭代过程中可以交替地估计块大小、块稀疏度和源信号,最后通过残差和估计信号的块稀疏度水平作为算法的终止条件。该算法在复杂度方面比多数算法略有提高,但所需先验知识少,重构概率高,在对实时性要求不太严格的情况下有较好的适用性。本文通过仿真实验验证了三种改进算法在块稀疏信号重构时的有效性。3.研究面向模拟信息转换的信号重构算法,重点针对多频带信号调制宽带转换器(Modulated Wideband Converter, MWC)采样系统的重构算法进行深入研究。目前对MWC采样系统的重构算法多数采用同步正交匹配追踪(Simultaneous Orthogonal Matching Pursuit, SOMP),针对目前SOMP算法效率低、重构概率不高等缺点,本文提出了一种修正信号支撑频带的同步子空间追踪算法,该算法每次迭代过程中对整个信号支撑频带进行同步估计,并在下一次迭代过程中利用最小均方准则进行估计信号支撑频带的修正,最终确定信号支撑频带,从而重构出源信号。对MWC采样系统重构的仿真实验表明,本文算法在复杂度和重构概率上较SOMP算法都有一定的优势,且本文算法的抗噪性能也较好,具有很好的适用性。更多还原

【Abstract】 Compressed Sensing (CS) is one emerging hotspot in signal processing. This technology employs a special samlping method which can capture and represent compressible signals at a rate significantly below the Nyquist rate, so there are wide application prospects in the areas of radar image, wireless sensor network (WSN), radio frequency communication, medical image processing, image device collecting and so on. One of the important tasks in CS is how to recover the signals more accurately and effectively, which is concerned by many researchers.With the basic theory of CS, the recovery algorithms are discussed in this dissertation. Aimed to improve the recovery probability and reducing the complexity, firstly, this dissertation summarizes several recovery algorithms, especially the matching pursuit (MP) type algorithms in detailed. And then, the recovery algorithms for block-sparse signals are studied. Finally, the dissertation researches the recovery algorithms for analog to information converter (AIC). Simulation results demonstrate the effectiveness of our algorithms. The main contents and research contributions of this dissertation are listed as follows:1.The MP type algorithms especially orthogonal matching pursuit (OMP) are studied. To solve the problem that the support set couldn’t be estimated accurately in standard OMP, a modified OMP using correlation coefficient is proposed. The basic idea of the algorithm is that the support set is searched by calculating correlation coefficients between the sensing matrix and the measurement vector instead of inner product. The correlation coefficient can describe the matching level better than inner product, so the proposed algorithm can determine the support set more accurately, which leads to high recovery probability. Simulation results show the proposed algorithm outperforms the standard OMP both on 1-D and 2-D signals.2.Block CS recovery algorithms are studied. Focous on the problems that the most existing block CS recovery algorithms are of low accuracy, high complexity and require some prior, this dissertation proposes three improved algorithms. Firstly, based on the subspace and backtracking idea, a block-sparse subspace matching pursuit algorithm has been proposed. The algorithm determines an estimate of the correct support set during each iteration, and the estimate support set will be refined at next iteration using the backtracking. Compared with the most existing algorithms, our algorithm has high recovery probability and low computational complexity. Subsequently, to solve the problem that the most existing recovery algorithms require block sparsity as prior knowledge, a block sparsity adaptive iteration algorithm has been proposed when the block sparsity is unknown. The proposed algorithm initializes a block sparsity which will increase by steps, until the exact support set and original signal are acquired. The complexity of this algorithm equals to some existing block CS recovery algorithms, but this algorithm doesn’t require block sparsity as a prior and has high recovery probability. Finally, for the shortcoming that the most block CS recovery algorithms require the block size and block-sparsity as a prior, this dissertation proposes a block-sparse adaptive matching pursuit algorithm. The most innovation of the proposed algorithm lies in the idea initializing the block size and block sparsity which can alternatively estimate the block size, block sparsity and the target signal. Compared with some existing algorithms, the complexity of this algorithm is a little high, but the proposed algorithm require less prior knowledge, and has high recovery probability, which can be applied in some non-real time problems. Simulation results show that the three presented algorithm is valid in recovery target source.3 . The recovery algorithms for AIC, especially modulated wideband converter (MWC) of multiband signals are studied. Most conventional MWC recovery algorithms employ simultaneous orthogonal matching pursuit (SOMP), which is ineffient and of low recovery probability. To solve the problem, a recovery algorithm which can refine the frequency support occupies is proposed in this dissertation, termed the simultaneous subspace pursuit. The proposed algorithm can estimate the whole frequency support occupy during each iteration, moreover, the frequency support occupies can be refined during next iteration using least mean square criterion. The recovery signal can be determined when the correct support band will be found. Compared with the SOMP, the proposed algorithm has low computational complexity, high recovery probability and good anti-noise performance. Simulation results for the practice multiband signals demonstrate its good performance.更多还原