基于压缩感知的医学图像测量矩阵及重构算法研究

发布时间：2018-01-11 01:07

本文关键词：基于压缩感知的医学图像测量矩阵及重构算法研究　出处：《吉林大学》2014年硕士论文　论文类型：学位论文

【摘要】：现代信号处理应用领域中，随着信息技术的快速发展，使得数据量与日俱增，以奈奎斯特定理为指导的采样方式导致采样率过大，硬件系统难以实现，不能满足实际的需要。医学成像需要对病人的病变部位进行反复扫描获取采样数据以重构图像，而长时间的扫描会给病人带来较高的辐射甚至不适，因而寻求用较少的采样数据精确重建出医学图像的方法，成为医学图像处理领域的研究热点。 2006年，Candes等人提出压缩感知理论(Compressed sensing, CS)，CS理论打破传统奈奎斯特定理采样率的束缚，通过设计一定的采样矩阵，对信号进行稀疏测量，再通过重构算法对图像进行稀疏重建。CS理论在采样同时对数据进行压缩，实现了低采样率数据重构。本文的主要工作和创新在于： 1、本文深入分析CS理论在医学图像重构中应用的可行性和合理性，分析了CS理论成功应用于医学图像的本质条件——医学图像良好的稀疏性，在此基础上，本文重点研究了压缩感知理论的两个关键技术——测量矩阵和重构算法，通过对常用测量矩阵和基本重构算法的深入研究和分析，分别对测量矩阵和重构算法提出了有效的改进，使医学成像在重构质量和重构时间两方面均有所提高。 2、本文介绍了目前常用的测量矩阵的构造方式和基本结构，并在采用相同的重构算法条件下，对多幅医学图像进行了压缩感知重构实验，对重构效果进行了评价分析；针对测量矩阵的特性，提出了基于奇异值分解的测量矩阵优化方法，然后用优化后的矩阵作为压缩感知测量矩阵对医学图像进行重构，实验结果表明，经过奇异值修正的矩阵与原矩阵相比较，重构时间相当的条件下，重构效果明显增强，，峰值信噪比提高1~2dB。 3、本文对目前主要的两大类压缩感知重构算法——贪婪算法和凸优化算法进行了梳理和介绍，深入研究了重构算法基本思想和实现步骤，并对每种算法的优缺点进行了验证、评价和对比分析。提出一种新的基于最小全变分的医学图像重构算法——SP_TV算法，该算法结合子空间匹配追踪(SP)算法重构速度快和最小全变分(TV)算法重构效果好的优点，实验结果表明，改进后的重构算法在重构效果和重构时间上均有明显提高。
[Abstract]:In the field of modern signal processing application, with the rapid development of information technology, the amount of data is increasing day by day. The sampling method guided by Nyquist theorem leads to too large sampling rate, and the hardware system is difficult to realize. Medical imaging can not meet the actual needs. Medical imaging needs to repeatedly scan the lesions of patients to obtain sampling data in order to reconstruct the image, and long time scanning will bring high radiation and even discomfort to the patients. Therefore, it has become a research hotspot in the field of medical image processing to seek a method to reconstruct medical image accurately with less sampling data. In 2006, Candes et al put forward the compressed sensing theory, CS theory breaks the shackles of the traditional Nyquist theorem sampling rate. By designing a certain sampling matrix, the signal is measured sparsely, and then the sparse reconstruction. CS theory is used to compress the data at the same time. The main work and innovation of this paper are as follows: 1. This paper deeply analyzes the feasibility and rationality of CS theory applied in medical image reconstruction, and analyzes the essential condition of successful application of CS theory in medical image-the good sparsity of medical image. On this basis, this paper focuses on the two key technologies of compressed sensing theory, measurement matrix and reconstruction algorithm, through the in-depth study and analysis of common measurement matrix and basic reconstruction algorithm. Both the measurement matrix and the reconstruction algorithm are improved effectively, so that the reconstruction quality and the reconstruction time of the medical imaging are improved. 2. This paper introduces the construction method and basic structure of the measurement matrix which is commonly used at present, and carries on the compression perception reconstruction experiment to many medical images under the condition of the same reconstruction algorithm. The effect of reconstruction is evaluated and analyzed. According to the characteristics of the measurement matrix, an optimization method of the measurement matrix based on singular value decomposition is proposed, and then the optimized matrix is used as the compressed sensing measurement matrix to reconstruct the medical image. Compared with the original matrix modified by singular value, the reconstruction effect is obviously enhanced and the peak signal-to-noise ratio (PSNR) is increased by 1 ~ 2 dB under the condition that the reconstruction time is equal to that of the original matrix. 3. In this paper, two main kinds of compressed perceptual reconstruction algorithms, greedy algorithm and convex optimization algorithm, are reviewed and introduced, and the basic ideas and implementation steps of the reconstruction algorithm are deeply studied. The merits and demerits of each algorithm are verified, evaluated and compared. A new medical image reconstruction algorithm based on minimum total variation, SPSP _ TV algorithm, is proposed. The algorithm combines the advantages of fast reconstruction speed and good reconstruction effect of the subspace matching tracking (SPV) algorithm. The experimental results show that the proposed algorithm is effective. The reconstruction effect and time of the improved reconstruction algorithm are improved obviously.
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN911.73

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