【作者】 伍政华；

【导师】 沈毅；

【作者基本信息】 哈尔滨工业大学 ， 控制科学与工程， 2011， 硕士

【摘要】 本文在深入研究压缩感知基本理论的同时,将压缩感知理论应用于盲源信号分离和光声成像。测量矩阵和恢复算法的设计是压缩感知的两大核心问题,首先从希尔伯特空间的基本性质和框架的定义入手深入分析了一个序列组可作为压缩感知观测向量组所需满足的条件,并据此引出了设计压缩感知测量矩阵的两个基本准则,即RIP条件和列相关性条件。然后在介绍了一些常见测量矩阵的同时,分析了包括随机测量矩阵和确定性测量矩阵在内的测量矩阵的优缺点。最后列举了两类算法中四种有代表性的恢复算法之后,通过大量的仿真实验全面比较这些算法的性能,并分析了这些算法各自的优势。现有的大多数盲源分离方法都需要过量测量和很多先验知识,针对这一现状将压缩感知应用于盲源信号分离,该方法所需的信息量是欠定的。通过对欠定的盲源分离的一般模型中信息的重组建立了与压缩感知之间的联系,并提出了盲源分离中线性算子的设计需求。最后通过对稀疏随机信号和真实语音信号进行仿真实验来验证所提出的方法。本文受到单像素相机设计原理的启发,用压缩感知原理设计了光声数据的采集模式,较已有的方法而言,其优势在于只需要较少的观测角度和观测数据就能达到传统方法的重建效果。根据光声数据在采集过程中会被噪声污染这一事实,将贝叶斯压缩感知算法应用于光声图像重建,实验结果表明这种方法有很好的重建效果。最后采用多角度融合的方法提高了成像分辨率。更多还原

【Abstract】 Based on the in-depth study of the basic theory of Compressed Sensing, we apply the theory to blind source separation and photoacoustic imaging reconstruction.The design of measurement matrix and recovery algorithm is the two core issues of Compressed Sensing. We first analyze what kind of sequences can be used as observation vectors by the basic properties of Hilbert space and tight frame, and thus leads to the two basic criteria of measurement matrix design: restricted isometry property (RIP) and the coherence of measurement matrix. Then we introduce some random matrices and deterministic matrices and analyze their advantages and disadvantages. After we list several algorithms of Compressed Sensing, a large number of simulation experiments are carried out to compare the performance of these algorithms.Most of the existing methods for blind source separation (BSS) require much prior knowledge and many measurements, aiming at this actuality, Compressed Sensing is proposed to separate blind sources which requires undersampled data. We analyze some similarities between CS and BSS, furthermore, the relationship between them is built by equivalent transformation. And then we analyze how to design the momentous operator of BSS and give some valuable conclusions. At last, sparse random signals and real sound signals are applied to verify the effectiveness of the whole framework.The photoacoustic data acquisition mode we design based on Compressed Sensing is prompted by the single-pixel camera. To have the same performance of traditional methods, the new mode requires only a few number of angles and observations. According to the fact that photoacoustic data is always polluted by noise data, we use Bayesian Compressed Sensing to reconstruct the photoacoustic imaging, the results of simulation experiments show that this algorithm has a good performance on photoacoustic imaging reconstruction. At last, by the multi-angle observation, it can reduce the number of measurements to improve the time resolution for a needed high-quality reconstruction image.更多还原