基于虚拟线圈和GRAPPA增强网络的PMRI方法
PMRI Image Reconstruction Method Based on Virtual Coils and GRAPPA-enhanced Network
通讯作者: * Tel: 19966188275, E-mail:zhanzhang@ie.ah.cn.
收稿日期: 2025-02-24 网络出版日期: 2025-04-23
| 基金资助: |
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Corresponding authors: * Tel: 19966188275, E-mail:zhanzhang@ie.ah.cn.
Received: 2025-02-24 Online: 2025-04-23
并行磁共振成像(PMRI)是一种通过多个接收线圈进行欠采样的成像技术,它利用空间信息补充梯度相位编码不足,通过特定算法重建无混叠图像,从而加速成像过程. 针对基于特定扫描的PMRI算法在有限数量的自动校准信号(ACS)下使用较高的加速因子会出现过拟合或泛化能力差的问题,提出一种基于虚拟线圈和GRAPPA增强网络的重建方法. 该方法通过使用虚拟共轭线圈扩充样本,并利用GRAPPA算法获得增强的ACS进行非线性的深度学习网络训练. 实验结果表明,提出的PMRI方法在较少ACS数量与较高加速因子的情况下,能够有效减少由于参考数据不足引起的混叠伪影,从而显著提高图像重建质量.
关键词:
Parallel magnetic resonance imaging (PMRI) is an imaging technique that uses multiple receiver coils for undersampling. It utilizes spatial information to supplement the insufficient gradient phase encoding and reconstructs aliasing-free images with specific algorithms to accelerate the imaging process. To address the issue of overfitting or poor generalization when using high acceleration factors with a limited number of auto calibration signals (ACS) in PMRI algorithms based on specific scans, a reconstruction method based on virtual coils and GRAPPA-enhanced networks is proposed. This method expands the sample by using virtual conjugate coils and enhances the ACS using the GRAPPA algorithm for training a nonlinear deep learning network. Experimental results show that the proposed PMRI method can effectively reduce aliasing artifacts caused by insufficient reference data, significantly improving image reconstruction quality with fewer ACS and higher acceleration factors.
Keywords:
本文引用格式
高照耀, 张展, 胡亮亮, 许光宇, 周胜, 胡雨欣, 林子捷, 周超.
GAO Zhaoyao, ZHANG Zhan, HU Liangliang, XU Guangyu, ZHOU Sheng, HU Yuxin, LIN Zijie, ZHOU Chao.
引言
磁共振成像(Magnetic Resonance Imaging,MRI)是一种利用强磁场和无线电波成像的医学影像技术,由于其不依赖于电离辐射(如X射线),因此相较于CT扫描和传统X光,具有更高的安全性,被广泛用于临床诊断和医学研究之中[1]. 虽然MRI技术在图像质量和诊断精度上具有无可替代的优势,然而其较长的扫描时间也给临床应用发展带来了挑战. 并行磁共振成像(Parallel Magnetic Resonance Imaging,PMRI)技术通过同时使用多个接收线圈来加快数据采集过程,缩短扫描时间,并在提高患者舒适度的同时,保持较高的图像质量,在多个临床应用场景中展现出巨大潜力[2]. 例如,磁共振心脏成像(Cardiac MRI,CMRI)需要使用心电门控并要求患者屏息,PMRI技术通过缩短扫描时间、减少屏息次数,提升了CMRI的可行性和舒适度,同时在儿童、老年人、无法保持静止的患者及急症场景中,降低了因长时间扫描而导致的运动伪影风险,提高了图像质量和诊断准确性. 合理的利用快速采集技术不但可以缩短MRI的检查时间,还可以大大提高检查质量,是当今磁共振技术发展的主流方向之一[3].
大多数临床扫描PMRI方法是利用灵敏度编码(Sensitivity Encoding,SENSE)[4]和广义自动校准部分并行采集(Generalized Auto Calibrating Partially Parallel Acquisitions,GRAPPA)[5]. 其中SENSE是一种基于图像域的并行成像方法,通过预扫描获取多个接收线圈的灵敏度图(Sensitivity Map),并结合这些信息来加速数据采集和图像重建. 而GRAPPA是一种基于K空间插值的并行成像算法,它通过使用自校准的部分采样数据来填补K空间中的缺失部分,从而加速扫描过程. 在GRAPPA的基础上,Zhao等[6]提出了基于GRAPPA的迭代重建方法,通过迭代地应用GRAPPA重新估计相位编码线并细化权重,从而减少了并行成像伪影. 此外,虚拟线圈概念(Virtual Coil Concept,VCC)不需要额外的物理硬件支持,通过数学建模生成额外接收通道,能够提升并行成像技术的加速因子,缩短扫描时间,并改善图像质量,在快速成像和高分辨率成像等应用场景中,虚拟线圈技术具有巨大的潜力. 例如Blaimer等[7]通过应用VCC到GRAPPA重建中,显著提升了并行成像技术的加速因子,实现了4~7倍加速成像. Wang等[8]利用磁共振线圈数据的复数共轭对称性质扩展了多层同时激发成像(Simultaneous Multi-Slice Imaging,SMS)所获取的多通道数据,实现了高质量的SMS图像重建.
近年来,随着深度学习技术的迅速发展,其在MRI中的应用逐渐得到深入探索. 目前为止,MRI重建的关键方法主要依赖于在大量数据集上进行训练,通常需要基于完全采样的数据构建大型训练数据库[9,10]. 由于训练过程对数据的需求量非常大,缺乏足够的高质量医学影像数据可能导致训练效果不理想,甚至可能导致重建图像的质量下降. 因此,如何有效利用有限的医学影像数据并提升重建精度,成为当前MRI重建研究中的一大挑战. 为了解决普遍性和数据可用性问题,Akçakaya等[11]提出了一种基于K空间插值的鲁棒性人工神经网络(Scan-specific Robust Artificial-neural-networks for K-space Interpolation,RAKI). 该算法无需借助外部数据库,而是通过利用特定扫描过程中额外采集的自动校准信号(Auto Calibration Signal,ACS)作为参考数据,进行欠采样数据与完整采样数据之间的映射学习,利用这种映射关系对欠采样的K空间进行恢复并重建. 基于RAKI算法的框架,Zhang等[12]提出了基于K空间插值的残差鲁棒人工神经网络(Residual Scan-specific Robust Artificial-neural-networks for K-space Interpolation,rRAKI). 该方法通过跳跃连接将非线性卷积神经网络(Convolutional Neural Network,CNN)与线性卷积结合,实现了针对特定扫描的深度学习网络重建,有效提高了图像重建的质量,并有效减小了高欠采样率下的卷褶伪影问题.
在PMRI中,理论上可实现的最大加速因子通常受到接收线圈数量的限制. 当前,二维MRI中常见的加速因子一般为2~4倍,随着加速因子的增加,较少的网络训练ACS参考数据可能导致噪声的显著放大,进而影响重建结果的质量[13]. 而较多的ACS会大幅度增加扫描时间. 在机器学习领域,针对有限训练数据的问题,常采用增强[14]、迁移学习[15]、生成对抗网络[16]学技术策略. 如何在ACS数量有限的情况下尽量提高加速倍率是亟待解决的问题[17-
1 理论与方法
1.1 VCC原理
VCC是一种在MRI领域中用于并行成像技术的创新概念,旨在通过数学模型或算法模拟出额外的接收线圈,从而提高成像速度和图像质量,而不需要物理上增加实际的线圈. 这种技术的核心在于利用现有的线圈信号和空间信息,通过算法合成出“虚拟”的接收通道,以优化并行成像过程,以此来减小噪声放大对重建图像质量的影响[7]. 具体来说,从线圈
其中,
其中*表示复共轭运算. 根据(2)式,信号可以被解释为来自一个虚拟线圈的信号,该线圈具有复敏感度分布
1.2 GRAPPA重建原理
图1
通常,在重建线圈
上式中
1.3 RAKI重建原理
RAKI通过使用多个紧凑型CNN代替传统的线性卷积核,从而实现对特定扫描任务的非线性K空间插值. 算法的训练流程如图2所示. 具体而言,ACS在按照输入数据的欠采样率
图2
1.4 本文提出的网络框架
针对训练数据较为有限情况下的磁共振并行成像问题,本文提出了一种结合虚拟共轭线圈与GRAPPA增强网络的PMRI方法,其总体架构如图3所示.
图3
该方法的核心组成部分包括虚拟共轭线圈生成器、GRAPPA模块以及rRAKI网络. 具体而言,虚拟共轭线圈生成器首先利用输入的均匀欠采样K空间数据生成扩展数据,然后通过GRAPPA模块对扩展数据进行线性K空间插值,从而获得扩展增强的ACS. 这些增强后的ACS数据被输入到深度学习网络中进行训练,以建立输入数据与目标数据之间的映射关系. 网络部分
1.5 损失函数
所提算法所采用的损失函数为
其中,
1.6 所提方法伪代码表述
伪代码表示如下所示:
(1)对于一组多通道磁共振均匀欠采样数据
(2)利用磁共振K空间虚拟共轭特性生成多一倍的欠采样数据
(3)使用GRAPPA算法利用
(4)通过截取
(5)设迭代上限
(6)根据设置的迭代上限
(7)迭代训练循环完成后,获得的多通道插值数据
2 实验与结果分析
2.1 实验数据
为了验证所提方法的有效性,本研究使用了合肥综合性国家科学中心能源研究院自主研发的7 T MRI系统实机采集的K空间数据样本进行性能评估. 实验使用的为健康的小鼠,年龄约为8~10周,体重大约300~350 g. 通过快速自旋回波(FSE, Fast Spin Echo)序列对实验鼠进行约100次不同平面的扫描,序列的回波时间(Echo Time,TE)为39.87 ms,重复时间(Repetition Time,TR)为3 000 ms,切片厚度为1.0 mm,回波链长度(Echo Train Length,ETL)为8,扫描方向覆盖横断位(Axial)、矢状位(Sagittal)和冠状位(Coronal),激发次数(Number of Excitations,NEX)为2,以确保高质量的解剖图像. 单次扫描数据包含8个通道,每个通道采集样本的空间分辨率为
2.2 评价指标
本文采用了三种常用的图像质量评价指标对网络重建结果进行了评价,分别为标准化均方根误差(Normalized Root Mean Squared Error,NRMSE)、峰值信噪比(Peak Signal-to-Noise Ratio,PSNR)和结构相似度指数(Structural Similarity,SSIM). 这些指标能够从不同角度全面反映重建图像的质量,涵盖了误差度量、信号保真度以及结构一致性等方面的评价标准.
NRMSE是均方误差(Mean Squared Error,RMSE)的归一化版本,旨在将误差相对于信号的幅度进行标准化. 它的计算公式为:
其中,
PSNR是衡量重建图像与原始图像之间信噪比的指标,通常用于评估图像压缩质量. 其计算公式为:
其中,
SSIM是一种评估两幅图像之间结构相似性的指标,考虑了亮度、对比度和结构三个方面. 其公式为:
其中,
2.3 实验环境与超参数设置
训练和测试过程在基于NVIDIA GeForce GTX 1050 Ti显卡(4GB显存)的计算平台上进行.
在实验设置中,首先设置了GRAPPA算法的参数,根据实验,卷积核较低会使得GRAPPA重建结果出现过多未插值的数据行,而过大的卷积核(大于10×10)使得重建速度过慢,综合考虑设置卷积核大小为(8, 8),表示使用8×8的卷积核来进行插值操作;正则化因子设置为0.01,用于平衡数据拟合与平滑解之间的权重,从而避免过拟合. 对于深度学习网络参数,其中批次大小(Batch Size)为20,并采用Adam优化器进行参数优化,初始学习率设置为0.01. 此外,为了动态调整学习率,使用了StepLR学习率调度器. 在预定的训练轮次(Epoch)为15、40和45时,学习率将乘以衰减因子0.1,以实现逐步降低学习率的效果. 整个训练过程共进行100个epochs,每个epoch包含30次迭代,确保充分的模型训练和收敛.
2.4 实验结果
为了说明虚拟线圈扩充与GRAPPA增强方法对线圈灵敏度估计的提升效果,分别对ACS增强前后的线圈灵敏度图进行了展示. 在7 T MRI采集样本上,未使用所提方法前的欠采样K空间ACS数目为24,加速因子为8. 对ACS中间24×24区域的数据进行灵敏度计算,得到的8通道线圈灵敏度图如图4所示. 灵敏度计算过程如下:首先,利用该ACS区域,通过尺寸为m×m的滑动窗口提取各线圈数据,构造校准矩阵
图4
图5
在合肥综合性国家科学中心能源研究院7 T MRI采集样本(通过快速自旋回波序列采集的健康小鼠脑部横断位、冠状位和矢状位解剖图样本)上,对所提方法与其他先进重建方法进行了比较,测试条件包括不同的ACS数目和不同的R,测试结果如表1所示. 针对同一小鼠,我们分别获取了其在横断位、冠状位和矢状位上的数据. 文中所展示结果为每个解剖方位进行多次重复实验后计算的平均值,最优值已加粗显示. 实验结果表明,所提方法在各项性能指标上均表现出色,尤其在低ACS数目下,例如ACS = 10,R = 5,相比于rRAKI方法,所提方法的NRMSE显著降低了88.43%,SSIM提高了21.70%,PSNR提高了33.99%. 这些结果表明,所提方法通过虚拟共轭线圈生成额外的训练数据,并结合GRAPPA方法扩展了自动校准信号的数量,从而增强了数据的多样性和规模,这一改进有效提升了模型的泛化能力和鲁棒性,使得重建结果在图像质量上取得了显著提高.
表1 不同算法的评价指标对比结果
Table 1
| ACS | R | 算法 | NRMSE | SSIM | PSNR |
|---|---|---|---|---|---|
| 16 | 4 | ZF | 0.3311 | 0.8475 | 23.8473 |
| GRAPPA | 0.0240 | 0.9248 | 35.2355 | ||
| RAKI | 0.0757 | 0.9282 | 30.2510 | ||
| rRAKI | 0.0702 | 0.9391 | 30.5825 | ||
| 本文方法 | 0.0108 | 0.9679 | 38.6888 | ||
| 10 | 5 | ZF | 0.6210 | 0.7924 | 21.1159 |
| GRAPPA | 0.0787 | 0.8544 | 30.0844 | ||
| RAKI | 0.2532 | 0.7941 | 25.0115 | ||
| rRAKI | 0.1954 | 0.7880 | 26.1367 | ||
| 本文方法 | 0.0226 | 0.9547 | 35.0208 | ||
| 18 | 6 | ZF | 0.2651 | 0.8599 | 24.2725 |
| GRAPPA | 0.1346 | 0.8069 | 27.7540 | ||
| RAKI | 0.0714 | 0.9071 | 29.9671 | ||
| rRAKI | 0.0967 | 0.8927 | 28.6522 | ||
| 本文方法 | 0.0229 | 0.9518 | 34.8806 | ||
| 24 | 8 | ZF | 0.3113 | 0.8669 | 24.1142 |
| GRAPPA | 0.1516 | 0.8021 | 27.2378 | ||
| RAKI | 0.1941 | 0.8215 | 26.1653 | ||
| rRAKI | 0.0984 | 0.8536 | 29.1153 | ||
| 本文方法 | 0.0599 | 0.9205 | 31.2673 | ||
| 30 | 10 | ZF | 0.3365 | 0.8723 | 23.7771 |
| GRAPPA | 0.1391 | 0.8205 | 27.6127 | ||
| RAKI | 0.2295 | 0.8084 | 25.4376 | ||
| rRAKI | 0.1906 | 0.7841 | 26.2441 | ||
| 本文方法 | 0.0982 | 0.9323 | 29.1251 | ||
| 30 | 15 | ZF | 0.3021 | 0.8749 | 24.1621 |
| GRAPPA | 0.1606 | 0.8219 | 26.9897 | ||
| RAKI | 0.2651 | 0.8748 | 24.7297 | ||
| rRAKI | 0.1834 | 0.8605 | 26.3309 | ||
| 本文方法 | 0.0781 | 0.9231 | 30.0419 |
为了直观比较本文提出的算法与其他对比算法在重建效果上的表现,我们从小鼠脑部实验的多层扫描数据中随机选取了一层冠状位原始采集数据,并对ACS = 10、R = 5,以及ACS = 30、R = 10的均匀欠采样数据进行了重建. 重建结果及其误差图如图6所示. 其中,ground-truth表示未经欠采样处理的原始图像数据,zero-filling则指将欠采样数据进行零填充处理后的图像. 每个ground-truth图像下方展示的是相应的均匀欠采样K空间数据,各个算法重建结果图像下方则呈现了与ground-truth图像相减得到的误差图. 误差图中的三个数值分别为通过重建图与参考图像计算得到的PSNR、SSIM和NRMSE指标.
图6
图6
不同算法重建结果和误差图
Fig. 6
Reconstruction results and error maps of different algorithms
通过对各算法重建结果的深入分析可见,基于深度学习的RAKI和rRAKI方法在训练数据较少的情况下,其重建图像存在明显的波浪形伪影,并且在细节恢复方面表现较差,导致重建图像与原始图像之间的差异较大. 相比之下,GRAPPA算法能够较好地减少伪影的产生,但重建图像中的噪声水平较高,误差图上表现出明显的噪声干扰. 与此不同,本文所提出的方法在较少的训练数据条件下,能够有效抑制伪影并较好地保留细节信息,重建图像在细节恢复和噪声控制方面表现优异,保持了与原始非欠采样图像较高的一致性. 总体而言,在训练数据较少的情况下,基于深度学习的重建算法往往面临更显著的性能退化问题,然而,所提方法能够在这些挑战性条件下保持较高的重建质量,不仅能够有效恢复图像细节,且误差较小,显示出更为优异的重建性能和较强的抗噪声能力. 进一步证明了其在更高加速因子的MRI图像重建任务中的适应能力.
2.5 消融实验
以基础的三层RAKI网络结构为基准,本研究通过逐步集成所提方法中的各个新组件,评估其在不同ACS数目和不同R条件下对整体重建性能的影响. 实验结果如表2所示,随着更多组件的引入,网络的重建性能得到了显著改善:具体而言,整体的NRMSE呈现持续下降趋势,PSNR持续上升,在ACS数量为10,R为2或者ACS数量为16,R为4的情况下各个组件对SSIM的指标影响不大,其它情况下,残差结构与虚拟共轭线圈生成对SSIM指标影响不大,但是迭代训练方法使SSIM的指标提升幅度较大. 这一结果验证了虚拟共轭线圈生成和迭代训练方法在提升模型重建性能方面的有效性. 特别地,在较少的ACS数量和较高加速因子的组合下(例如,ACS数目为10、R为5),引入迭代训练策略后,SSIM和PSNR显著提高了21.24%和46.01%,而NRMSE则显著降低至6.85%. 这一改善表明,迭代训练方法通过结合线性重建技术扩展ACS,并通过循环训练不断优化模型参数,能够有效提升模型在高加速因子和低ACS情况下的重建效果,显著提高了图像重建质量.
表2 消融实验对比结果
Table 2
| ACS | R | 残差结构 | 虚拟共轭 线圈生成 | 迭代训练方法 | NRMSE | SSIM | PSNR |
|---|---|---|---|---|---|---|---|
| 10 | 2 | × | × | × | 0.0032 | 0.9847 | 42.8324 |
| √ | × | × | 0.0031 | 0.9850 | 42.8832 | ||
| √ | √ | × | 0.0024 | 0.9855 | 43.9197 | ||
| √ | √ | √ | 0.0020 | 0.9797 | 44.7016 | ||
| 10 | 5 | × | × | × | 0.1985 | 0.7845 | 24.9643 |
| √ | × | × | 0.1857 | 0.7850 | 25.0925 | ||
| √ | √ | × | 0.1684 | 0.7834 | 25.5169 | ||
| √ | √ | √ | 0.0136 | 0.9512 | 36.4516 | ||
| 16 | 4 | × | × | × | 0.1456 | 0.9185 | 26.1477 |
| √ | × | × | 0.0962 | 0.9460 | 27.9456 | ||
| √ | √ | × | 0.0202 | 0.9693 | 34.7181 | ||
| √ | √ | √ | 0.0084 | 0.9489 | 38.5150 | ||
| 24 | 8 | × | × | × | 0.2910 | 0.7816 | 23.1409 |
| √ | × | × | 0.2798 | 0.7844 | 23.3122 | ||
| √ | √ | × | 0.2347 | 0.7927 | 24.0741 | ||
| √ | √ | √ | 0.0349 | 0.9246 | 32.3490 | ||
| 30 | 10 | × | × | × | 0.4402 | 0.6674 | 21.3433 |
| √ | × | × | 0.2402 | 0.7993 | 23.9745 | ||
| √ | √ | × | 0.2131 | 0.7791 | 24.4926 | ||
| √ | √ | √ | 0.1285 | 0.9233 | 26.6901 |
3 结论
针对基于特定扫描的并行成像算法在有限数量的训练数据下出现混叠伪影的问题,提出了基于虚拟线圈和GRAPPA增强网络的PMRI方法. 其中,虚拟共轭线圈生成方法是利用磁共振K空间数据共轭对称的特性,生成原线圈采集数据的共轭对称数据,为原有数据提供了额外的相位敏感度信息;GRAPPA增强网络结合了GRAPPA和标准RAKI方法的优点,在应对更高加速因子和更少训练数据的情况下,展现出了较强的潜力,能够很好地抑制磁共振并行成像在较高加速因子情况下的噪声和残留伪影,从而获得更优的重建效果. 由于本文所提方法依赖于GRAPPA算法的插值结果输入到深度学习网络中进行训练,而GRAPPA算法的参数需要通过经验进行设置,这些参数可能并非最优值,因此可能对后续的深度学习训练产生影响. 未来的研究可以进一步优化这一流程,通过深度学习网络自动调节GRAPPA算法的参数,并实现二者更好的结合,从而提高重建结果的质量.
利益冲突
无
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