【作者】 郝鹏鹏；

【导师】 练秋生；

【作者基本信息】 燕山大学 ， 电路与系统， 2009， 硕士

【摘要】 传统的Nyquist采样定理要求采样频率必须大于等于信号最高频率的两倍,但很多情况下信号带宽较大,采样频率达不到最高频率的两倍。最近Donoho和Candès提出了压缩传感CS(Compressed Sensing)理论。该理论利用原始信号或图像的稀疏性先验知识,通过合适的优化算法,可由少量的采样值或观测值来进行重建。目前该理论的研究尚处于初级阶段,大多是基于压缩传感基础理论的研究和一维信号的重建。本文将压缩传感理论应用于图像重建中,针对其重建速度慢和重建质量不高的缺点,在深入研究现有算法的基础上,从以下几方面进行研究:(1)基于压缩传感和代数重建法的CT(Computed Tomography)重建结合压缩传感理论提出了一种基于代数重建法ART(Algebraic Reconstruction Technique)的高质量CT图像重建算法。该算法将CT图像的梯度稀疏性结合到ART图像重建中,在每次迭代中的投影操作结束后用梯度下降法调整全变差,减小图像梯度的1范数。实验结果表明了该算法的有效性。(2)基于全变差多种范数的核磁共振图像重建利用核磁共振图像具有梯度和边缘稀疏性的先验知识来加快其成像速度,提出了一种基于全变差的核磁共振图像重建算法,并对1、p (0 < p< 1)与log和惩罚函数三种范数进行了实验和比较分析。(3)基于线性Bregman和混合基稀疏表示的压缩传感图像重建提出了一种基于离散余弦变换和双树复数小波两种基混合的图像稀疏表示,利用线性Bregman迭代来进行重建的压缩传感系统。该算法在每一次迭代更新后用梯度下降法进行全变差调整,再分别在两种基上执行软阈值处理来减小图像的1范数。实验结果表明该算法有效提高了重建图像的质量。更多还原

【Abstract】 The convertional Nyquist sampling theory requires the sampling frequency must at least twice the highest frequency of signal, but in many cases it doesn’t achieve the requirement, because of the large bandwidth. Recently Donoho and Candès have proposed compressed sensing theory, which applies the sparsity prior of the signals or images and can accurately reconstruct original signals or images from a small quantity of measurements, provided an appropriate optimizd procedure. At present the study of CS is still in the first stage, most of studies are about the basic theory and the recovery of one dimensional signal. Aimed at the disadvantage of the slow rcovered speed and the bad recovered quality, we apply the compressed sensing to the image reconstruction, in the foundation of the deeper research on the existing methods, and mainly research on the following aspects in this paper:(1) Image reconstruction for CT based on compressed sensing and ART. We make use of the compressed sensing theory, and propose a method based on ART to improve the quality of the recovered image and the speed of reconstruction. The method, which combines the gradient sparsity of CT images and ART, reduces the 1 norm of the image gradient by regulating the total variation with the gradient descend method after completing the projection on the corresponding hyperplane in each iteration. The experimental results show the effectivity of the method.(2) Sparse MRI reconstruction via multiple norms based on total variation. The compressed sensing makes use of the gradient and edge sparsities which are implicit in MR images to quicken the imaging speed. We propose a new MRI reconstruction method based on total variation, and then perform the experiments on 1, p (0 < p< 1) and log-sum penalty function and compare their performance.(3) Compressed sensing image reconstruction based on linearized Bregman and mixed bases sparse representation. We propose a compressed sensing system based on the sparse representation of images on discrete cosine transform and the dual tree complex wavelet transform, making use of the linearized Bregman iteration to reconstruct the original image. The method regulates the total variation with the gradient descend method after updating in each iteration, and then performs the soft-thresholding on these two bases respectively to reduce the 1 norm of the image. The results of experiments show that our method effectively improves the quality of the recovered image.更多还原