A geomagnetic reference map reconstruction method based on sparse representation and dictionary learning
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摘要:
地磁匹配导航在导航制导领域具有重要作用，地磁基准图的构建精度决定了地磁匹配导航的有效性。针对现有地磁基准图构建精度难以满足实际应用需求的问题，提出了基于稀疏表示和字典学习的高精度地磁基准图构建方法。首先，利用矩谐分析(RHA)进行稀疏字典的初始化；其次，利用K-SVD算法对稀疏字典进行训练；最后，利用低分辨率和高分辨率基准图具有相同稀疏系数的特点重建高分辨率地磁基准图。实验结果表明：所提方法对地磁基准图具有更高的构建精度，对训练所需的数据集有更低的需求，同时对噪声有更好的鲁棒性。与PSO-Kriging插值法相比，在4倍放大倍数下峰值信噪比(PSNR)由26.31 dB提高至26.73 dB，结构相似度(SSIM)由0.498提高至0.524，均方根误差(RMSE)由14.96 nT减小至13.78 nT。
Abstract:Geomagnetic matching navigation plays an important role in the field of navigation guidance. The construction accuracy of geomagnetic reference map determines the effectiveness of geomagnetic matching navigation. Aimed at the problem that the existing geomagnetic reference map construction accuracy is difficult to meet the needs of practical applications, a high-precision geomagnetic reference map construction method based on sparse representation and dictionary learning is proposed. First, the sparse dictionary is initialized using Rectangular Harmonic Analysis (RHA). Then, K-SVD is used to train the sparse dictionaries. Finally, the feature that the low-resolution and high-resolution reference maps have the same sparse coefficients is used to reconstruct the high-resolution geomagnetic reference maps. Experimental results show that the proposed method has higher construction accuracy for geomagnetic reference maps, lower requirements for training datasets, and better robustness to noise. Compared with the PSO-Kriging interpolation method, with a magnification factor of 4, the Peak Signal to Noise Ratio (PSNR) value is increased from 26.31 dB to 26.73 dB; the Structural Similarity Index (SSIM) is increased from 0.498 to 0.524; the Root Mean Square Error (RMSE) is decreased from 14.96 nT to 13.78 nT.
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图 2 基于稀疏表示和字典学习的地磁基准图超分辨率重建方法流程
Figure 2. Flowchart of super-resolution geomagnetic reference map reconstruction method based on sparse representation and dictionary learning
图 4 四倍放大倍数下地磁基准图重建效果对比
Figure 4. Comparison of geomagnetic reference map reconstructed with magnification factor 4
图 5 三倍放大倍数下训练数据集大小对有/无先验信息字典重建基准图PSNR值的影响
Figure 5. Effect of training dataset size on reconstructed reference map PSNR of dictionaries with and without priori information with magnification factor 3
图 6 三倍放大倍数下训练数据集大小对有/无先验信息字典重建基准图SSIM值的影响
Figure 6. Effect of training dataset size on reconstructed reference map SSIM of dictionaries with and without priori information with magnification factor 3
图 7 三倍放大倍数下训练数据集大小对有/无先验信息字典重建基准图RMSE值的影响
Figure 7. Effect of training dataset size on reconstructed reference map RMSE of dictionaries with and without priori information with magnification factor 3
表 1 二倍放大倍数下不同方法PSNR、SSIM和RMSE指标对比
Table 1. Comparison of PSNR, SSIM and RMSE of different methods with magnification factor 2
方法 PSNR/dB SSIM RMSE/nT 双三次插值法 32.16 0.789 3.07 相邻嵌入法 32.14 0.787 3.12 PSO-Kriging插值法 32.31 0.796 2.89 本文方法 32.44 0.823 2.77 
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表 2 三倍放大倍数下不同方法PSNR、SSIM和RMSE指标对比
Table 2. Comparison of PSNR, SSIM and RMSE of different methods with magnification factor 3
方法 PSNR/dB SSIM RMSE/nT 双三次插值法 27.66 0.565 7.65 相邻嵌入法 27.59 0.561 7.83 PSO-Kriging插值法 28.28 0.606 7.23 本文方法 28.54 0.637 6.91
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表 3 四倍放大倍数下不同方法PSNR、SSIM和RMSE指标对比
Table 3. Comparison of PSNR, SSIM and RMSE of different methods with magnification factor 4
方法 PSNR/dB SSIM RMSE/nT 双三次插值法 24.89 0.431 16.77 相邻嵌入法 24.81 0.435 16.47 PSO-Kriging插值法 26.31 0.498 14.96 本文方法 26.73 0.524 13.78
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表 4 不同噪声等级下各种方法PSNR值对比
Table 4. Comparison of PSNR of different methods under different noise levels
方法 PSNR/dB σ=0 σ=3 σ=6 σ=9 σ=12 双三次插值法 28.89 28.80 28.45 28.17 27.74 相邻嵌入法 28.84 28.73 28.47 28.13 27.86 PSO-Kriging插值法 29.35 29.30 29.21 29.11 28.97 本文方法 29.78 29.76 29.73 29.69 29.67
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表 5 不同噪声等级下各种方法SSIM值对比
Table 5. Comparison of SSIM of different methods under different noise levels
方法 SSIM σ=0 σ=3 σ=6 σ=9 σ=12 双三次插值法 0.603 0.587 0.573 0.551 0.533 相邻嵌入法 0.599 0.584 0.571 0.555 0.541 PSO-Kriging插值法 0.637 0.626 0.611 0.597 0.581 本文方法 0.664 0.661 0.659 0.658 0.654
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表 6 不同噪声等级下各种方法RMSE值对比
Table 6. Comparison of RMSE of different methods under different noise levels
方法 RMSE/nT σ=0 σ=3 σ=6 σ=9 σ=12 双三次插值法 9.72 9.83 9.96 10.14 10.30 相邻嵌入法 9.81 9.89 9.99 10.12 10.24 PSO-Kriging插值法 9.11 9.20 9.31 9.44 9.61 本文方法 8.77 8.82 8.85 8.89 8.95
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