基于正则化方法的磁共振图像去噪与重建技术的研究

发布时间：2018-11-01 12:24

【摘要】：磁共振成像(Magnetic Resonance Imaging,MRI)技术因其无电离辐射,诊断信息丰富等优势在医疗领域发挥着重要的作用。然而,磁共振仪器直接获取到的图像信号往往会受到噪声、采集方式等因素的影响而产生退化现象。从获取的退化信号中恢复原始信号可通过正则化求逆来进行。正则化方法所构建的数学模型由确保数据一致性的误差项和正则化约束项组成,其中,如何构造先验约束项是影响图像复原质量的重要因素。本课题对基于正则化方法的磁共振图像去噪和重建模型进行了研究,深入分析和探讨了其建立到求解的过程。首先,在磁共振图像的去噪方面,本文以达到较好的去噪效果并尽可能地降低去噪过程的计算复杂度为核心目标,研究了对全变分(Total Variation,TV)做出改进的几种高阶方法,通过具体实验探讨了它们各自的优势,并针对传统高阶全变分(Higher Degree Total Variation,HDTV)求解方法复杂度较高求解耗时长的缺点提出了一种快速最大值-最小值(Fast Majorization-Minimization,FMM)算法,通过引入辅助变量进行交替求解,使计算效率提高了5-7倍,实现了质量与效率兼顾的高阶全变分正则化去噪这一目的。其次,本文对基于压缩感知理论(Compressed Sensing,CS)的正则化磁共振图像重建方法进行了研究。在对经典正则化模型的研究基础上,本文提出了一种混合正则化方法来实现对图像的自适应稀疏促进,在高倍数欠采样的情况下实现更高质量的磁共振图像重建。在二维图像的模拟实验中,混合正则化方法能够达到优于现有对比方法的重建质量。此外,本文将其进行了理论扩展,用于三维图像的重建中,通过实验对比发现混和正则化能够重建出效果更佳的三维磁共振图像。最后,在动态磁共振成像方面,由于动态图像数据冗余度较大,可采用CS-MRI技术对其进行欠采样重建,从而实现高效率的图像获取。本文延用了对静态图像所提出的混合正则化重建方法,将其与时间域上的低秩方法相结合,针对动态磁共振成像提出了低秩-混合全变分(Low Rank-Combined HDTV,LR-CHDTV)正则化方法,实现了在高成像加速倍数下重建出高质量的动态磁共振图像这一目标。
[Abstract]:Magnetic resonance imaging (Magnetic Resonance Imaging,MRI) technology plays an important role in medical field because of its advantages of non-ionizing radiation and abundant diagnostic information. However, the image signals directly obtained by magnetic resonance instruments are often affected by noise, acquisition methods and other factors, resulting in degradation phenomenon. The restoration of the original signal from the acquired degenerate signal can be done by regularizing the original signal. The mathematical model constructed by the regularization method consists of error terms and regularization constraints to ensure the consistency of data. Among them, how to construct a priori constraint term is an important factor affecting the quality of image restoration. In this paper, the model of Mr image denoising and reconstruction based on regularization method is studied, and the process of establishing and solving the model is analyzed and discussed. Firstly, in the aspect of denoising of magnetic resonance image, aiming at achieving better denoising effect and reducing the computational complexity of denoising process as far as possible, several high-order methods to improve total variation (Total Variation,TV) are studied. Their respective advantages are discussed through specific experiments, and a fast Max-Minimum (Fast Majorization-Minimization,FMM) algorithm is proposed to solve the problem that the complexity of the traditional high-order total variational (Higher Degree Total Variation,HDTV (Higher Degree Total Variation,HDTV) method is high and time-consuming. By introducing auxiliary variables to solve the problem alternately, the computational efficiency is improved 5-7 times, and the goal of high order total variational regularization denoising is realized, which takes both quality and efficiency into account. Secondly, the regularized Mr image reconstruction method based on compressed perception theory (Compressed Sensing,CS) is studied in this paper. Based on the study of the classical regularization model, a hybrid regularization method is proposed to achieve the adaptive sparse enhancement of the image and the reconstruction of the magnetic resonance image with higher quality under the condition of high multiple under-sampling. In the simulation experiment of 2D images, the hybrid regularization method can achieve better reconstruction quality than the existing contrast methods. In addition, the theory is extended to reconstruct 3D images. The results of experiments show that mixing regularization can reconstruct 3D MRI images with better results. Finally, in the aspect of dynamic magnetic resonance imaging, because of the large redundancy of dynamic image data, CS-MRI technology can be used for under-sampling and reconstruction to achieve high efficiency image acquisition. In this paper, the hybrid regularization method for static images is extended and combined with the low rank method in time domain. For dynamic magnetic resonance imaging, a low rank mixed total variational (Low Rank-Combined HDTV,LR-CHDTV) regularization method is proposed. The goal of reconstruction of high quality dynamic magnetic resonance images with high imaging acceleration is achieved.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP391.41

【参考文献】