基于紧标架加权稀疏约束的磁共振图像重建
Tight Frame based Weighted Sparse Reconstruction for Magnetic Resonance Image
答辩人：胡榆涵
指导老师：屈小波 教授/博导
答辩委员会主席：董继扬 教授 博导 厦门大学电子科学系
答辩委员会成员：包立君 副教授 硕导 厦门大学电子科学系
林建忠 主任医师 硕导 厦门大学附属中山医院影像科
答辩秘书：王 新 高级工程师 厦门大学电子科学系
时间：2021年05月25日上午10:00
地点：厦门大学海韵园科研二-313
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摘要
磁共振成像(Magnetic Resonance Imaging，MRI)是无创和无放射性的成像方法，被广泛地应用于临床诊断中。但过长的扫描时间难以捕获信号的快速变化，对于有运动的部位成像容易产生伪影。因此，减少数据的扫描时间，同时获取高质量的磁共振图像是学术界和工业界的目标。基于压缩感知的磁共振成像(Compressed Sensing MRI，CS-MRI)是加速MRI的重要方式。CS-MRI的关键之一是图像的稀疏表示，主要分为正交稀疏表示和冗余稀疏表示，后者以紧标架为代表。基于紧标架的稀疏重建能够捕捉更多的图像特征，从而更好地抑制噪声和伪影。紧标架稀疏表示下包括综合型和分解型两种重建模型，后者已被前人验证表明重建误差更低。对于分解型重建模型的求解，屈小波等人提出了一种简单高效的投影快速迭代阈值算法(projected Fast Iterative Soft-thresholding Algorithm，pFISTA)。但是，目前关于pFISTA的研究集中于笛卡尔欠采样稀疏重建，对于非笛卡尔欠采样稀疏重建问题及应用尚未涉及。
动态对比度增强成像(Dynamic Contrast-enhanced MRI，DCE-MRI)能够表征组织的形态学特征和微血管血流动力学特征，被广泛地用于肿瘤严重等级检测以及靶向药疗效评估中。传统笛卡尔采样的DCE时间分辨率较低，难以捕捉到完整的动态变化。近年来，非笛卡尔黄金角放射线采样被用于实现高时间分辨率的DCE成像。但现有的一些重建方法重建时间较长，在加速因子(Acceleration Factor, AF)较高时出现重建图像误差高、噪声和伪影较多、动态定量参数如体积转移常数(Ktrans)和血浆体积分数(Vp)保真度较低等问题。
对于DCE成像，本文提出了时空分离加权稀疏约束重建模型，在模型中引入权重区分时间维冗余稀疏和空间维冗余稀疏各自的重要性。我们推导了pFISTA以适用于求解所提非笛卡尔重建模型，同时证明了pFISTA在非笛卡尔欠采样稀疏重建中的收敛性条件。在脑肿瘤DCE和腹部DCE数据上的重建结果均表明，所提方法在快速采样的相对较高AF下，可以获得最低的重建误差和最高的图像结构相似度。此外，所提方法能更快地重建腹部DCE数据，可以提高脑肿瘤数据的动态定量参数Ktrans和Vp的保真度。
对于静态磁共振成像，现有的基于紧标架的重建模型未区分不同的稀疏系数，会导致图像细节丢失。因此，本文提出了加权冗余稀疏分解型重建模型，引入权重区分静态图像在稀疏变换域稀疏系数各自的重要性。我们推导了pFISTA以适用于求解所提模型，同时证明了pFISTA在加权l1范数约束重建中的收敛性条件。实测脑部数据实验结果表明，所提方法在不同的欠采样模板和不同的采样率下均实现了最低的重建误差。
关键词：磁共振成像；动态对比度增强磁共振成像；非笛卡尔黄金角放射线采样；加权稀疏重建；快速算法
ABSTRACT
Magnetic Resonance Imaging (MRI) is a non-invasive and non-radioactive imaging method, which is widely used in clinical diagnosis. However, long scanning time is difficult to capture the rapid signal changes, and will lead to artifacts in the imaging of moving parts. Therefore, reducing scanning time while obtaining high-quality magnetic resonance (MR) images is the goal of academia and industry. Compressed Sensing MRI (CS-MRI) is an important way to accelerate MRI. One of the key points of developing CS-MRI reconstruction methods is the sparse representation. Sparse representation can be divided into two main categories: orthogonal sparse representation system and redundant sparse representation system. The latter is mainly represented by tight frame which can capture more image features to better suppress noise and artifacts. Under tight frame sparse representation, there are two different models called synthetic model and analysis model. The latter can achieve lower reconstruction error. To solve the analysis model, Qu et al proposed a simple and efficient algorithm named projected fast iterative soft-thresholding algorithm (pFISTA). However, current research on pFISTA mainly concentrated on the reconstruction under Cartesian under-sampling. The reconstruction problem and application under the non-Cartesian under-sampling have not been involved.
Dynamic contrast-enhanced MRI (DCE-MRI) can evaluate the morphological characteristics and microvascular hemodynamic characteristics. It has been widely used to detect tumor severity and evaluate treatment response of targeted drugs. Traditional Cartesian sampling for DCE leads to low time resolution and cannot capture complete dynamic changes. In recent years, non-Cartesian golden-angle radial sampling has been used to achieve DCE-MRI with high temporal resolution. However, existing methods remains long reconstruction time. Besides, under high acceleration factor (AF), these methods suffer from high reconstruction error, much noise and artifacts, and low fidelity of dynamic quantitative parameters Ktrans and Vp.
For DCE-MRI, this thesis proposed a spatiotemporal separation weighted sparse reconstruction model. Weights were introduced to distinguish the importance of spatial and temporal sparsity. We derived pFISTA to be suitable for solving the proposed non-Cartesian reconstruction model and theoretically proved the convergence condition of pFISTA under non-Cartesian reconstruction. Results on both the brain tumor DCE and liver DCE show that, at relatively high AF, the lowest reconstruction error and highest image structural similarity are obtained by the proposed method. Besides, the proposed method achieves faster reconstruction for liver datasets and better physiological measures on brain tumor images.
For static MRI, the existing tight frame-based reconstruction models do not distinguish different sparse coefficients, which leads to the loss of image details. Therefore, this thesis proposed a weighted sparse reconstruction model. Weights were introduced to distinguish the importance of the sparse coefficients in sparse transform domain. We derived pFISTA to be suitable for solving the proposed model and proved the convergence condition of pFISTA under weighted l1 norm reconstruction. Experimental results on brain data show that the proposed method achieves the lowest reconstruction errors under different under-sampling patterns and sampling rates.
Key words：MRI; DCE-MRI; Non-Cartesian golden-angle radial sampling; Weighted sparse reconstruction; Fast algorithm
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