基于各向异性扩散的GRAPPA重建算法

摘要论文题目：基于各向异性扩散的医学图像分割技术研究专业：计算机应用技术研究生：吴颖指导教师：陈家新教授摘要图像分割是医学图像处理中的关键技术之一，也是三维重建、定量分析等后续操作的基础，分割的效果直接影响到三维重建的速度和重建后模型的视觉效果。

然而，由于医学图像本身的模糊性和复杂性，以及医学影像设备（如CT、MRI等）成像技术上的特点，使得医学图像存在一定的噪声，图像中目标物体部分边缘也有可能局部不清晰，这导致医学图像分割成为一个经典的难题。

本文从图像滤波的角度入手，结合医学图像分割方法，设计出了相应的改进算法。

首先，由于各向异性扩散算法是一种选择性的非线性滤波算法，根据图像内容的不同而采取不同的平滑方式，但是它对医学图像的细节边缘特征保持效果不太理想。

针对这一问题，本文提出一种基于形态学的各向异性扩散滤波算法。

设计了一种自适应加权的多尺度形态滤波来改进扩散系数，并引入K值估计法，从而达到去除噪声和增强边缘的双重效果；同时采用一个简单实用的迭代终止准则，避免了迭代次数的设定。

其次，分水岭算法是一种应用广泛的图像分割算法，它可以快速、准确地获取图像的边缘，但易受噪声和量化误差的影响，导致过分割现象。

本文采用上述改进后的各向异性扩散算法对原始图像进行预处理，并引入多尺度的形态梯度图像作为分水岭变换的参考图像，来突出图像中物体的边界轮廓，平滑具有均匀亮度的区域，同时定义一个基于边界平均灰度和面积的区域合并准则，对分割后的区域进一步合并。

最后，通过实验对上述算法进行了验证，并与已有算法进行对比分析。

实验结果表明：改进后的各向异性扩散滤波算法，在提高信噪比的同时又可保留重要的微细结构，可以较好地满足医学图像的使用要求；本文改进的分水岭分割算法能有效抑制过分割，同时具有较强的抗噪声性能，得到的分割结果满足医学图像建模的需要。

关键词：图像分割，数学形态学，各向异性扩散，分水岭算法河南科技大学硕士学位论文论文类型：应用研究摘要Subject: Research on Medical Image Segmentation Based on Anisotropic DiffusionSpecialty: Computer Applications TechnologyName: WU YingSupervisor: Professor CHEN Jia-xinABSTRACTMedical image segmentation is a crucial step in image processing, and then, which is the precondition of 3D reconstruction and quantify analysis. With the development of medical imaging, image segmentation takes more important role in medical application. Medical image has the complexity and diversity, as well as the characteristic of imaging technology of medical image equipment, which make it being some noise and logical blurring of edges and details. So it becomes classical problem in medical image process and analysis.Firstly, our methods are developed on the image filtering, combining anisotropic diffusion and image segmentation algorithms, two improved algorithms are designed. The improved anisotropic diffusion filtering algorithm is proposed according to the disadvantages of Perona-Malik model. The novel diffusion model is established based on morphological diffusion coefficient, which adopts multi-scale morphological filter with auto-adapted determinations weights. The improved scheme has superiority capability over the PM scheme. Also an iteration stopping criterion is adopted to avoid computing the times.Secondly, the watershed is a kind of mathematical morphologic image segmentation. It get the precise edge which is continues, closing and single-pixel. The main disadvantage of watershed transform is the over-segmentation due to its sensitive to noise. A novel medical image segmentation algorithm based on anisotropic diffusion filtering using watershed transformation is proposed. Getting the input image through adaptive anisotropic diffusion filter, and then, a multi-scale morphological grads image is obtained as the input of watershed algorithm. At the same time, judging rules are defined based on the average edge gray and area of segmentation region, which are used for region-merging.Lastly, the dissertation has realized the two algorithms with MATLAB. We use a lot of models to validate and analyze them and to compare with the existed algorithm河南科技大学硕士学位论文results, which prove the improved algorithms are available. It has been shown from the experiments that the first method can improve SNR, and at the same time it can retain important details structure, as well as, the improved watershed algorithm is very simple, and can restrain the over-segmentation phenomena effectively, so can obtain good segmentation results.KEY WORDS: Image Segmentation, Mathematical Morphologic, Anisotropic Diffusion, Watershed AlgorithmDissertation Type: Research on Application缩略语词汇表缩略语词汇表CT - Computerized Tomography 计算机断层扫描成像MRI - Magnetic Resonance Imaging 磁共振成像2D - Two Dimensional 二维3D - Three Dimensional 三维PDE - Partial Differential Equation 偏微分方程SNR - Signal to Noise 信噪比PSNR - Peak Signal-to-Noise Ratio 峰值信噪比MSE - Mean Standard Error 均方误差EPI - Edge Preserve Index 边缘保持指数第1章绪论第1章绪论1.1 课题背景和研究意义近年来，随着计算机及其相关技术的迅速发展及图形图像技术的日渐成熟，并逐渐渗入到医学领域中，数字医疗的新时代已经到来。