基于稀疏表示和字典学习的地磁基准图构建方法

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。 

A geomagnetic reference map reconstruction method based on sparse representation and dictionary learning

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.