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摘要:
二维(2D)多切片磁共振数据在相邻切片之间具有高度的相关性，通过利用切片间的冗余性能够重建出更高质量的切片图像，但由于硬件条件的限制，2D多切片磁共振成像（MRI）需要耗费大量时间。为提高2D多切片磁共振图像的重建质量和重建速度，将联合稀疏变换学习正则项引入到多切片Hankel张量完成（MS-HTC）模型中，提出一种快速2D多切片磁共振成像重建（FMS-JTLHTC）算法。该算法使用交替方向乘子法对目标问题进行求解；引入快速迭代收缩阈值法加快收敛，并使用图形处理器对算法进行加速。使用4组脑部数据集在2种不同采样模式下进行实验，结果表明：FMS-JTLHTC算法的峰值信噪比（PSNR）相较于同时自动校准和K空间估计（SAKE）算法、并行成像数据的局部K空间领域的低秩建模（PLORAKS）算法和MS-HTC算法分别平均提高了4.04 dB、3.67 dB和2.07 dB，而且重建速度相比MS-HTC算法提高了14倍。
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关键词:
- 多切片磁共振成像 /
- Hankel张量完成 /
- 联合稀疏变换学习 /
- 交替方向乘子法 /
- 快速迭代收缩阈值法
Abstract:Due to the significant correlation between neighboring slices in two-dimensional (2D) multi-slice magnetic resonance data, higher quality slice pictures can be reconstructed by taking use of the redundancy between slices. However, 2D multi-slice magnetic resonance imaging requires an amount of time. To improve the reconstruction quality and speed of 2D multi-slice (MRI) images, proposes a fast 2D multi-slice MRI reconstruction (FMS-JTLHTC) algorithm, which introduces the joint transform learning regular term into the multi-slice hankel tensor completion (MS-HTC) model. Prior to introducing the fast iterative shrinkage-thresholding procedure to accelerate convergence and utilize the graphics processing unit to speed up the procedure, the alternating direction method of multipliers is used to solve the objective issue. Experiments using four brain datasets in two different sampling modes show that the peak signal-to-noise ratio (PSNR) of the FMS-JTLHTC algorithm is improved by an average of 4.04 dB, 3.67 dB, and 2.07 dB compared to the simultaneous atuo-calibrating and K-space estimation (SAKE), low-rank modeling of local K-space neighborhoods with parallel imaging data (PLORAKS) and MS-HTC algorithms, respectively, the reconstruction speed is improved by a factor of 14 compared to the MS-HTC algorithm.
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图 1 4种算法对AF=5的1D-VRDU采样模式下的dataset 1重建的图像和误差图
Figure 1. Images and error maps of dataset 1 reconstruction by four algorithms for 1D-VRDU sampling pattern with AF=5
图 2 4种算法对AF=10的2D-VRDU采样模式下dataset 2重建的图像和误差图
Figure 2. Images and error maps of dataset 2 reconstruction by four algorithms for 2D-VRDU sampling pattern with AF=10
图 3 4种算法对AF=3的1D-Poisson欠采样模式下datase 1重建的图像和误差图
Figure 3. Images and error maps of dataset 1 reconstruction by four algorithms for 1D-Poisson undersampling mode with AF=3
图 4 FMS-JTLHTC算法与其他算法对不同加速因子的2种采样模式下4个数据集重建图像的PSNR的差值箱线图
Figure 4. Boxplot of difference in PSNR between FMS-JTLHTC algorithm and other algorithms for reconstructed images of four datasets with different acceleration factors for two sampling patterns
图 5 数据集dataset 3在2种采样模式下进行重建的收敛性分析
Figure 5. Convergence analysis of dataset dataset 3 reconstructed in two sampling patterns
图 6 FMS-JTLHTC、rawFMS-JTLHTC和MS-HTC算法对4个数据集进行重建的时间比较
Figure 6. Comparison of reconstruction times of FMS-JTLHTC, rawFMS-JTLHTC and MS-HTC algorithms for four datasets
图 7 FMS-JTLHTC算法对5倍加速的1D-VRDU采样模式下dataset 1重建时参数$\alpha $和$ {\mu _1} $的变化对重构图像PSNR值的影响
Figure 7. Effect of variation of parameters $\alpha $ and $ {\mu _1} $ on PSNR values of reconstructed images during dataset 1 reconstruction by FMS-JTLHTC algorithm for 1D-VRDU sampling mode with 5-fold acceleration
图 8 FMS-JTLHTC和MS-JTLHTC算法对5倍加速的1D-VRDU采样模式下4个数据集重建时PSNR值随迭代次数的变化
Figure 8. Variation of PSNR values with number of iterations for four datasets reconstructed by FMS-JTLHTC and MS-JTLHTC algorithm with 5-fold acceleration of 1D-VRDU sampling mode
表 1 4种算法对不同加速因子的1D-VRDU采样模式下4个数据集重建的评价指标平均值
Table 1. Mean values of evalution indicators reconstructed by four algorithms for four datasets in 1D-VRDU sampling pattern with different acceleration factors
算法 AF PSNR/dB MSSIM FSIM HFEN SAKE[6] 3 32.86 0.9070 0.9961 0.2070 5 28.55 0.8370 0.9912 0.3126 6 27.66 0.8238 0.9889 0.3437 7 27.29 0.8062 0.9875 0.3680 PLORAKS[7] 3 33.85 0.9151 0.9973 0.1814 5 29.27 0.8489 0.9929 0.2892 6 28.11 0.8304 0.9906 0.3282 7 27.53 0.8154 0.9883 0.3659 MS-HTC[30] 3 35.19 0.9317 0.9981 0.1365 5 31.82 0.8844 0.9954 0.2083 6 31.32 0.8805 0.9949 0.2265 7 30.98 0.8711 0.9937 0.2416 FMS-JTLHTC 3 38.01 0.9646 0.9990 0.0997 5 34.59 0.9401 0.9981 0.1504 6 33.71 0.9318 0.9976 0.1698 7 33.39 0.9267 0.9973 0.1830 
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表 2 4种算法对不同加速因子的2D-VRDU采样模式下4个数据集重建的评价指标平均值
Table 2. Mean values of evalution indicators reconstructed by four algorithms for four datasets in 2D-VRDU sampling pattern with different acceleration factors
算法 AF PSNR /dB MSSIM FSIM HFEN SAKE[6] 3 37.89 0.9571 0.9996 0.0664 5 35.36 0.9326 0.9990 0.0980 8 33.48 0.9148 0.9984 0.1361 10 32.67 0.9068 0.9979 0.1609 12 32.09 0.8977 0.9974 0.1797 PLORAKS[7] 3 37.86 0.9537 0.9996 0.0657 5 35.55 0.9354 0.9991 0.0966 8 33.65 0.9168 0.9984 0.1354 10 32.83 0.9059 0.9979 0.1549 12 32.24 0.8987 0.9975 0.1730 MS-HTC[30] 3 38.55 0.9626 0.9997 0.0591 5 35.98 0.9435 0.9992 0.0850 8 34.21 0.9263 0.9987 0.1144 10 33.26 0.9136 0.9981 0.1343 12 32.92 0.9115 0.9979 0.1458 FMS-JTLHTC 3 39.99 0.9738 0.9997 0.0529 5 37.58 0.9619 0.9995 0.0722 8 35.76 0.9497 0.9992 0.0951 10 34.94 0.9435 0.9989 0.1094 12 34.34 0.9383 0.9988 0.1203
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表 3 4种算法对AF=3的1D-Possion欠采样模式下数据集dataset 1重建的评价指标值
Table 3. Values of evalution indicators for four algorithms for reconstruction of dataset dataset 1 in 1D-Possion undersampling pattern with AF=3
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表 4 5种算法对AF=5的1D-VRDU采样模式下4个数据集的重建时间与速度
Table 4. Reconstruction times and velocities of five algorithms for four datasets in 1D-VRDU sampling mode with AF=5
算法 t/s 速度提升倍数 Dataset 1 Dataset 2 Dataset 3 Dataset 4 Dataset 1 Dataset 2 Dataset 3 Dataset 4 SAKE[6] 779.35 779.50 779.39 779.17 44.82 36.79 32.14 23.62 PLORAKS[7] 570.30 517.17 578.35 777.84 32.79 24.41 23.85 23.58 MS-HTC[30] 272.46 271.92 271.43 275.41 15.67 12.83 11.19 8.35 rawFMS-JTLHTC 456.81 550.35 624.76 860.09 26.27 25.97 25.76 26.07 FMS-JTLHTC 17.39 21.19 24.25 32.99 1.00 1.00 1.00 1.00
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表 5 5种算法对AF=10的2D-VRDU采样模式下四个数据集的重建时间与速度
Table 5. Reconstruction times and velocities of the five algorithms for four datasets in 2D-VRDU sampling mode with AF=10
算法 t/s 速度提升倍数 Dataset 1 Dataset 2 Dataset 3 Dataset 4 Dataset 1 Dataset 2 Dataset 3 Dataset 4 SAKE[6] 311.95 207.80 259.67 207.94 29.10 19.37 18.15 14.21 PLORAKS[7] 99.62 96.39 98.85 398.66 9.29 8.98 6.91 27.25 MS-HTC[30] 222.17 168.68 193.70 165.82 20.72 15.72 13.54 11.33 rawFMS-JTLHTC 282.55 281.26 376.39 374.50 26.32 26.21 26.30 25.60 FMS-JTLHTC 10.72 10.73 14.31 14.63 1.00 1.00 1.00 1.00
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