【作者】 李勇；

【导师】 冉启文；

【作者基本信息】 哈尔滨工业大学 ， 应用数学， 2011， 硕士

【摘要】 压缩传感是一种新型的稀疏采样方法。相对于经典的香农采样有两点不同,第一随机采样代替了一致均匀采样;第二在重建算法上,香农采样采用的是插值法来重建原始信号,而压缩采样是利用最优化算法,通过寻找最稀疏的采样,来重建原始信号。因此节省了先采样后压缩的过程,也就是说压缩传感整合了采样和压缩,节省了不必要的存储,对于实际工程有潜在的应用。本文研究了压缩传感的重建算法,压缩传感的重建算法有两个主要部分,分别是信号的稀疏矩阵表示和测量矩阵。这里我们给出了几种稀疏矩阵的实例,首次提出用分数傅里叶变换作为稀疏表示的方法,并且分析了可行性,给出了测量矩阵满足的条件,并且归类举例说明了几种符合条件的测量矩阵模型。虽然压缩传感还是比较新的压缩理论,但是关于压缩传感的重建算法已经涌现了许多。为了提高压缩传感算法的实时性,有些人提出了分块压缩传感算法,但是分块压缩传感,对于每一块图像用的测量矩阵是相同的,也就是说每一块的重要程度,只与图像的像素数有关,但是没有考虑除像素外的其他因素。一幅图像的重要部分应该是图像的边缘部分,这是符合人的视觉特点的,而每一块图像的边缘比例是不一样的,所以重要程度自然不一样。因此本文基于人眼视觉的特点,提出了一种新的压缩传感重建算法,即加权分块压缩传感算法,并且将其应用到正交匹配追踪算法和全变差最小化算法。为了说明算法的有效性,我们进行了大量的数值实验。实验表明,加权分块压缩算法,相比图像未经过分块的压缩传感重建算法,实时性明显提高;相比分块压缩传感重建算法,图像重建后的峰值信噪比提高了近一分贝,处理效果也显著提高了。更多还原

【Abstract】 Compressed sensing is a new type of sparse sampling. There are two different aspects from the classical Shannon sampling. Firstly, it is random sampling instead of uniform sampling. Secondly, the interpolation is used in Shannon sampling while the algorithm of optimization in mathematic is used in the compressed sensing. It means the compressed sensing reconstructs the original signal by searching the least sparse sampling points. Hence it saves the process of compressing after sampling, that is to say, it integrates with the two processes. So it saves much more storage and will have potential application in the engineering.In this paper, we principally invest the algorithm of the compressed sensing, which includes two major parts, the sparse matrix and the measurement matrix respectively. We give some examples of the sparse matrix. Specially, we propose the fractional Fourier transform as the sparse representation of the original signal creatively and analyze its feasibility. Also we give the condition meeting the measurement matrix and exemplify some model of the measurement matrix.As a new theory, the reconstructed algorithm of compressed sensing emerges a lot recently. Some authors proposed the block compressed sensing in order to improve the real-time. However it used the same measurement matrix in every block of the image. It means the value of every block is not distinction except the amounts of the pixel. For an image, the edge is the important part, which is also the sensitive to mankind vision. The proportion of the edge in each block is different as so as the importance of each block. In this paper, we propose the weighted block compressed sensing based on mankind vision. Then we apply it to the orthogonal matching pursuit and minimization total variation. In order to verify the effectiveness of the algorithm, we perform a lot of numerical simulation. We show that the new method can improve the real-time comparing with the algorithm of compressed sensing without blocking and the PSNR nearly one decibel comparing with the algorithm of the block compressed sensing respectively.更多还原