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基于稀疏表示和字典学习的地磁基准图构建方法

马啸宇 张金生 李婷 郝亮亮

马啸宇, 张金生, 李婷, 等 . 基于稀疏表示和字典学习的地磁基准图构建方法[J]. 北京航空航天大学学报, 2021, 47(8): 1656-1663. doi: 10.13700/j.bh.1001-5965.2020.0263
引用本文: 马啸宇, 张金生, 李婷, 等 . 基于稀疏表示和字典学习的地磁基准图构建方法[J]. 北京航空航天大学学报, 2021, 47(8): 1656-1663. doi: 10.13700/j.bh.1001-5965.2020.0263
MA Xiaoyu, ZHANG Jinsheng, LI Ting, et al. A geomagnetic reference map reconstruction method based on sparse representation and dictionary learning[J]. Journal of Beijing University of Aeronautics and Astronautics, 2021, 47(8): 1656-1663. doi: 10.13700/j.bh.1001-5965.2020.0263(in Chinese)
Citation: MA Xiaoyu, ZHANG Jinsheng, LI Ting, et al. A geomagnetic reference map reconstruction method based on sparse representation and dictionary learning[J]. Journal of Beijing University of Aeronautics and Astronautics, 2021, 47(8): 1656-1663. doi: 10.13700/j.bh.1001-5965.2020.0263(in Chinese)

基于稀疏表示和字典学习的地磁基准图构建方法

doi: 10.13700/j.bh.1001-5965.2020.0263
基金项目: 

国家自然科学基金 61673017

中国博士后科学基金 2019M3643

详细信息
    通讯作者:

    张金生. E-mail: 18813059158@163.com

  • 中图分类号: V221+.3;TB553

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

Funds: 

National Natural Science Foundation of China 61673017

China Postdoctoral Science Foundation 2019M3643

More Information
  • 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。

     

  • 图 1  地磁参考场特征

    Figure 1.  Features of geomagnetic reference field

    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 3  K-SVD算法流程

    Figure 3.  Flowchart of K-SVD algorithm

    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
    下载: 导出CSV

    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
    下载: 导出CSV

    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
    下载: 导出CSV

    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
    下载: 导出CSV

    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
    下载: 导出CSV

    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
    下载: 导出CSV
  • [1] HOLLAND R A, THORUP K, VONHOF M J, et al. Navigation: Bat orientation using Earth's magnetic field[J]. Nature, 2006, 444(7120): 702. doi: 10.1038/444702a
    [2] ECKENHOFF K, GENEVA P, HUANG G. Direct visual-inertial navigation with analytical preintegration[C]//2017 IEEE International Conference on Robotics and Automation (ICRA). Piscataway: IEEE Press, 2017: 1429-1435.
    [3] CUNTZ M, KONOVALTSEV A, MEURER M. Concepts, development and validation of multi-antenna GNSS receivers for resilient navigation[J]. Proceedings of the IEEE, 2016, 104(6): 1-14. doi: 10.1109/JPROC.2016.2566740
    [4] LOHMANN K J, LOHMANN C M F, EHRHART L M, et al. Geomagnetic map used in seaturtle navigation[J]. Nature, 2004, 428(6986): 909-910. doi: 10.1038/428909a
    [5] 岳建平, 甄宗坤, 基于粒子群算法的Kriging插值在区域地面沉降中的应用[J]. 测绘通报, 2012(3): 59-62.

    YUE J P, ZHEN Z K. Application of particle swarm optimization based Kriging interpolation method in regional land subsidence[J]. Bulletin of Surveying and Mapping, 2012(3): 59-62(in Chinese).
    [6] 李晨霖, 王仕成, 张金生, 等. 基于改进的Kriging插值方法构建地磁基准图[J]. 计算机仿真, 2018, 35(12): 278-282.

    LI C L, WANG S C, ZHANG J S, et al. Construction of geomagnetic datum map based on improved Kriging interpolation method[J]. Computer Simulation, 2018, 35(12): 278-282(in Chinese).
    [7] GOLDENBERG F. Geomagnetic navigation beyond the magnetic compass[C]//Position, Location & Navigation Symposium. Piscataway: IEEE Press, 2006: 684-694.
    [8] AKESSON S, LUSCHI P, BRODERICK A C. Oceanic long-distance navigation: Do experienced migrants use the Earth's magnetic field [J]. Journal of Navigation, 2001, 54(3): 415-427. http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=86149&fulltextType=RA&fileId=S0373463301001473
    [9] LIN Y, YAN L, TONG Q. Underwater geomagnetic navigation based on ICP algorithm[C]//IEEE International Conference on Robotics and Biomimetics. Piscataway: IEEE Press, 2008: 2115-2120.
    [10] CAI Q, YANG G, SONG N, et al. Analysis and calibration of the gyro bias caused by geomagnetic field in a dual-axis rotational inertial navigation system[J]. Measurement Science and Technology, 2016, 27(10): 105001. doi: 10.1088/0957-0233/27/10/105001
    [11] LIU M, LIU K, YANG P, et al. Bio-inspired navigation based on geomagnetic[C]//IEEE International Conference on Robotics and Biomimetics. Piscataway: IEEE Press, 2013: 2339-2344.
    [12] GAO X, ZHANG K, TAO D, et al. Image super-resolution with sparse neighbor embedding[J]. IEEE Transactions on Image Processing, 2012, 21(7): 3194-3205. doi: 10.1109/TIP.2012.2190080
    [13] WANG G, LI L, LI Q. Perceptual evaluation of single-image super-resolution reconstruction[C]//2017 IEEE International Conference on Image Processing(ICIP). Piscataway: IEEE Press, 2017: 3145-3149.
    [14] ROMANO Y, ISIDORO J, MILANFAR P. RAISR: Rapid and accurate image super resolution[J]. IEEE Transactions on Computational Imaging, 2016, 3(1): 110-125. http://ieeexplore.ieee.org/document/7744595/
    [15] YEGANLI F, NAZZAL M, UNAL M, et al. Image super-resolution via sparse representation over multiple learned dictionaries based on edge sharpness[J]. Signal, Image and Video Processing, 2016, 10(3): 535-542. doi: 10.1007/s11760-015-0771-7
    [16] VILLENA S, VEGA M, BABACAN S D, et al. Bayesian combination of sparse and non-sparse priors in image super resolution[J]. Digital Signal Processing, 2013, 23(2): 530-541. doi: 10.1016/j.dsp.2012.10.002
    [17] LIU D, WANG Z, WEN B, et al. Robust single image super-resolution via deep networks with sparse prior[J]. IEEE Transactions on Image Processing, 2016, 25(7): 1. doi: 10.1109/TIP.2016.2585779
    [18] LEDIG C, THEIS L, HUSZAR F, et al. Photo-realistic single image super-resolution using a generative adversarial network[EB/OL]. (2017-05-25)[2020-05-28]. https://arxiv.org/abs/1609.04802.
    [19] FARHADIFARD F, ABAR E, NAZZAL M, et al. Single image super resolution based on sparse representation via directionally structured dictionaries[C]//Signal Processing and Communications Applications Conference (SIU). Piscataway: IEEE Press, 2014: 1718-1721.
    [20] QI N, SHI Y, SUN X, et al. Single image super-resolution via 2D sparse representation[C]//2015 IEEE International Conference on Multimedia and Expo (ICME). Piscataway: IEEE Press, 2016: 1-6.
    [21] 乔玉坤, 王仕成, 张金生, 等. 采用矩谐分析和支持向量机的地磁导航基准图构建方[J]. 西安交通大学学报, 2010, 44(10): 47-51.

    QIAO Y K, WANG S C, ZHANG J S, et al. A constructing method of reference maps for geomagnetic navigation using rectangular harmonic analysis and support vector machine[J]. Journal of Xi'an Jiaotong University, 2010, 44(10): 47-51(in Chinese).
    [22] YANG S, WANG M, CHEN Y, et al. Single-image super-resolution reconstruction via learned geometric dictionaries and clustered sparse coding[J]. IEEE Transactions on Image Processing, 2012, 21(9): 4016-4028. doi: 10.1109/TIP.2012.2201491
    [23] ZHANG Y, LIU Y. Single image super-resolution reconstruction method based on LC-KSVD algorithm[C]//1st International Conference on Materials Science, Energy Technology, Power Engineering(MEP 2017), 2017: 1-6.
    [24] YANG J, WRIGHT J, HUANG T S, et al. Image super-resolution as sparse representation of raw image patches[C]//2008 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Piscataway: IEEE Press, 2008: 1-8.
    [25] MOUSAVI H, MONGA V. Sparsity-based color image super resolution via exploiting cross channel constraints[J]. IEEE Transactions on Image Processing, 2017, 26(11): 5094-5106. doi: 10.1109/TIP.2017.2704443
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出版历程
  • 收稿日期:  2020-06-15
  • 录用日期:  2020-08-30
  • 刊出日期:  2021-08-20

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