Sensitivity encoding reconstruction algorithm based on multi-category dictionary learning
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摘要:
灵敏度编码(SENSE) 方法利用多个线圈的灵敏度信息来减少扫描时间，利用SENSE模型重构的图像易存在伪影，不利于医学诊断。为减少重叠伪影，提高磁共振成像质量，将分类图像块的快速正交字典引入SENSE模型中，得到一种基于多分类字典学习的灵敏度编码重建算法。该算法通过对图像块分类，在每个类中训练字典，得到不同类别的多个字典，运用交替方向乘子法进行图像重构。在人体脑部和膝盖数据上进行实验，结果表明：相比于TV-SENSE、TV-LORAKS-SENSE和LpTV-SENSE算法，所提算法的平均信噪比分别提高了1.53 dB、1.22 dB和1.05 dB，重构图像与参考图像的一致性较高，图像细节部分和边缘轮廓信息保留完整。
Abstract:The sensitivity encoding (SENSE) method explicitly utilizes sensitivity information from multiple receiving coils to reduce scan time. The images reconstructed using the SENSE model have a portion of blurring artifacts that are not conducive to medical diagnosis. We propose a sensitivity coding reconstruction approach based on multi-classification dictionary learning to minimize overlap artifacts and enhance the quality of parallel magnetic resonance imaging by integrating fast dictionary learning on classed patches into the SENSE model. In order to obtain picture reconstructions using alternating direction method of multipliers, the algorithm first classifies the image blocks and then trains multiple dictionaries of various classes in each category. The results on the human brain and knee data show that the algorithm improves the average signal-to-noise ratio by 1.53 dB, 1.22 dB and 1.05 dB over the TV-SENSE, TV-LORAKS-SENSE and LpTV-SENSE algorithms, respectively. The reconstructed image is in high agreement with the reference image, and the image detail part and edge contour information are kept intact.
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图 1 AF=5、24像素×24像素ACS二维泊松圆盘欠采样时4个数据的信噪比随时间变化曲线
Figure 1. SNR versus time curves for four data at two-dimensional Poisson discs undersampling when acceleration factor is 5 and 24 pixel×24 pixel ACS
图 2 AF=4时4种算法在欠采样数据1上的重构图像和误差
Figure 2. Reconstructed and error images for four algorithms on undersampled data 1 when acceleration factor is 4
图 3 AF=4时4种算法在欠采样数据2上的重构图像和误差
Figure 3. Reconstructed and error images for four algorithms on undersampled data 2 when acceleration factor is 4
图 4 AF=4时4种算法在欠采样数据3上的重构图像和误差
Figure 4. Reconstructed and error images for four algorithms on undersampled data 3 when acceleration factor is 4
图 5 AF=4时4种算法在欠采样数据4上的重构图像和误差
Figure 5. Reconstructed and error images for four algorithms on undersampled data 4 when acceleration factor is 4
图 6 22个数据在AF=3～7、24像素×24像素ACS 泊松圆盘欠采样时FDLCP-SENSE1与其他算法SNR的差值
Figure 6. SNR difference between FDLCP-SENSE1 and other algorithms for 22 data when acceleration factor is 3−7 and 24 pixel × 24 pixel ACS Poisson disc undersampling
图 7 AF=4时对欠采样数据3重构的收敛性分析
Figure 7. Convergence analysis of reconstruction on data 3 when acceleration factor is 4 under undersampling
表 1 AF=3～7时数据1在泊松圆盘欠采样下各算法的重构结果
Table 1. Reconstruction results of different algorithms for data 1 under Poisson disc undersampling when acceleration factor is 3−7
算法 SNR/dB SSIM HFEN AF=3 AF=4 AF=5 AF=6 AF=7 AF=3 AF=4 AF=5 AF=6 AF=7 AF=3 AF=4 AF=5 AF=6 AF=7 TV-SENSE[15] 24.06 22.40 20.97 20.05 19.07 0.9729 0.963 5 0.952 2 0.942 6 0.931 5 0.113 9 0.147 8 0.184 8 0.211 6 0.245 9 TV-LORAKS-SENSE[16] 23.80 22.32 21.10 20.24 19.28 0.970 0 0.960 8 0.951 0 0.942 6 0.932 2 0.108 6 0.139 4 0.171 6 0.196 3 0.230 0 LpTV-SENSE[17] 24.19 22.61 21.32 20.43 19.45 0.973 7 0.964 6 0.954 3 0.944 5 0.933 0 0.111 2 0.140 5 0.173 1 0.199 0 0.231 8 FDLCP-SENSE1 24.84 23.40 22.35 21.59 20.52 0.977 1 0.969 8 0.962 1 0.955 7 0.944 9 0.100 3 0.125 2 0.150 3 0.169 1 0.203 9 
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表 2 AF=3～7时数据2在泊松圆盘欠采样下各算法的重构结果
Table 2. Reconstruction results of different algorithms for data 2 under Poisson disc undersampling when acceleration factor is 3−7
算法 SNR/dB SSIM HFEN AF=3 AF=4 AF=5 AF=6 AF=7 AF=3 AF=4 AF=5 AF=6 AF=7 AF=3 AF=4 AF=5 AF=6 AF=7 TV-SENSE[15] 23.77 22.24 20.87 19.79 19.04 0.966 2 0.955 4 0.943 7 0.931 6 0.922 4 0.105 5 0.134 2 0.167 5 0.198 7 0.220 5 TV-LORAKS-SENSE[16] 23.97 22.57 21.40 20.31 19.62 0.967 1 0.957 1 0.947 7 0.937 1 0.928 8 0.092 9 0.115 7 0.142 5 0.170 9 0.190 8 LpTV-SENSE[17] 24.13 22.57 21.28 20.12 19.29 0.969 4 0.958 7 0.947 9 0.933 7 0.922 9 0.098 0 0.125 3 0.154 6 0.188 2 0.210 6 FDLCP-SENSE1 25.09 23.80 22.61 21.44 20.71 0.975 2 0.968 2 0.959 8 0.948 6 0.941 1 0.085 4 0.105 3 0.130 3 0.159 5 0.177 9
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表 3 AF=3～7时数据3在泊松圆盘欠采样下各算法的重构结果
Table 3. Reconstruction results of different algorithms for data 3 under Poisson disc undersampling when acceleration factor is 3−7
算法 SNR/dB SSIM HFEN AF=3 AF=4 AF=5 AF=6 AF=7 AF=3 AF=4 AF=5 AF=6 AF=7 AF=3 AF=4 AF=5 AF=6 AF=7 TV-SENSE[15] 27.78 26.32 25.41 24.58 23.77 0.981 4 0.976 2 0.972 5 0.969 1 0.965 0 0.075 5 0.091 8 0.105 6 0.118 4 0.133 2 TV-LORAKS-SENSE[16] 27.76 26.44 25.64 24.89 24.18 0.980 5 0.975 3 0.971 8 0.968 7 0.965 2 0.070 9 0.085 2 0.097 5 0.109 8 0.122 9 LpTV-SENSE[17] 27.85 26.48 25.64 24.98 24.25 0.980 9 0.975 6 0.971 8 0.968 8 0.965 1 0.074 5 0.088 8 0.101 2 0.110 4 0.123 8 FDLCP-SENSE1 28.63 27.47 26.72 26.15 25.51 0.984 1 0.979 9 0.976 9 0.974 3 0.971 5 0.065 9 0.077 2 0.087 4 0.095 8 0.105 3
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表 4 AF=3～7时数据4在泊松圆盘欠采样下各算法的重构结果
Table 4. Reconstruction results of different algorithms for data 4 under Poisson disc undersampling when acceleration factor is 3−7
算法 SNR/dB SSIM HFEN AF=3 AF=4 AF=5 AF=6 AF=7 AF=3 AF=4 AF=5 AF=6 AF=7 AF=3 AF=4 AF=5 AF=6 AF=7 TV-SENSE[15] 19.03 17.73 16.95 16.20 15.69 0.923 5 0.902 4 0.888 9 0.877 3 0.866 6 0.227 5 0.278 2 0.309 1 0.345 5 0.376 6 TV-LORAKS-SENSE[16] 19.15 17.95 17.25 16.59 16.08 0.924 2 0.903 6 0.891 1 0.880 8 0.870 9 0.201 9 0.250 2 0.276 9 0.309 5 0.341 1 LpTV-SENSE[17] 19.01 17.82 17.19 16.59 16.11 0.921 6 0.899 7 0.887 1 0.876 5 0.865 2 0.216 0 0.267 6 0.289 5 0.317 9 0.343 8 FDLCP-SENSE1 20.01 18.93 18.30 17.75 17.34 0.936 2 0.919 1 0.908 0 0.897 5 0.889 9 0.182 0 0.216 2 0.236 3 0.254 5 0.274 1
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表 5 AF=3～7时22个数据在泊松圆盘欠采样下平均SNR、平均SSIM、平均HFEN差值
Table 5. Difference of mean SNR, mean SSIM, and mean HFEN for 22 sets of data at Poisson disc undersampling when acceleration factor is 3−7
算法 平均SNR/dB 平均SSIM 平均HFEN AF=3 AF=4 AF=5 AF=6 AF=7 AF=3 AF=4 AF=5 AF=6 AF=7 AF=3 AF=4 AF=5 AF=6 AF=7 FDLCP-SENSE1 &
TV-SENSE1.23 1.44 1.61 1.68 1.71 0.055 6 0.072 1 0.082 3 0.090 6 0.097 2 −0.032 8 −0.045 4 −0.055 8 −0.063 9 −0.069 5 FDLCP-SENSE1 &
TV-LORAKS-SENSE0.85 1.06 1.26 1.43 1.51 0.007 1 0.009 8 0.012 3 0.014 0 0.015 3 −0.014 2 −0.026 5 −0.037 5 −0.049 4 −0.058 2 FDLCP-SENSE1 &
LpTV-SENSE0.86 1.01 1.10 1.13 1.14 0.029 6 0.038 2 0.043 2 0.047 5 0.050 6 −0.023 8 −0.031 4 −0.036 8 −0.041 5 −0.043 9
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表 6 AF=4时不同算法在欠采样的4个数据上的重构时间
Table 6. Reconstruction time of different algorithms on four data at undersampling when acceleration factor is 4
s 数据 TV-SENSE TV-LORAKS-
SENSELpTV-SENSE FDLCP-SENSE1 数据1 38 153 15 27 数据2 53 281 23 31 数据3 213 866 41 63 数据4 196 319 40 105
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