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低秩和联合平滑性约束下的时变海表面温度重构方法

李姣 万腾汶 邱伟

李姣, 万腾汶, 邱伟. 低秩和联合平滑性约束下的时变海表面温度重构方法[J]. 电子与信息学报. doi: 10.11999/JEIT240253
引用本文: 李姣, 万腾汶, 邱伟. 低秩和联合平滑性约束下的时变海表面温度重构方法[J]. 电子与信息学报. doi: 10.11999/JEIT240253
LI Jiao, WAN Tengwen, QIU Wei. Time-varying Sea Surface Temperature Reconstruction Leveraging Low Rank and Joint Smoothness Constraints[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT240253
Citation: LI Jiao, WAN Tengwen, QIU Wei. Time-varying Sea Surface Temperature Reconstruction Leveraging Low Rank and Joint Smoothness Constraints[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT240253

低秩和联合平滑性约束下的时变海表面温度重构方法

doi: 10.11999/JEIT240253
基金项目: 国家自然科学基金(42176197),湖南省自然科学基金(2022JJ40461),湖南省教育厅优秀青年项目(21B0301)
详细信息
    作者简介:

    李姣:女,副教授,研究方向为最优化方法及应用、生物分子计算

    万腾汶:女,硕士生,研究方向为最优化方法及应用

    邱伟:男,副教授,研究方向为稀疏信号重构、海洋信息处理

    通讯作者:

    邱伟 qiuwei08@nudt.edu.cn

  • 中图分类号: TN911.7

Time-varying Sea Surface Temperature Reconstruction Leveraging Low Rank and Joint Smoothness Constraints

Funds: The National Natural Science Foundation of China (42176197), The Natural Science Foundation of Hunan Province (2022JJ40461), The Excellent Youth Foundation of Education Bureau of Hunan Province (21B0301)
  • 摘要: 海表面温度对于海洋动力过程及海气相互作用等具有重要意义,是海洋环境关键要素之一。浮标是海表面温度观测的常用手段,但由于浮标在空间的分布不规则,浮标采集的海表面温度数据也呈现非规则性。另外,浮标在实际工作中难免存在故障,致使采集的海表面温度数据存在缺失。因此对存在缺失的非规则海表面温度数据进行重构具有重要意义。该文通过将海表面温度数据建立为时变图信号,利用图信号处理方法解决海表面温度缺失数据重构问题。首先,利用数据的低秩性和时域-图域联合变差特性构建海表面温度重构模型;其次,基于交替方向乘子法框架提出一种求解该优化模型的基于低秩和联合平滑性(LRJS)的时变图信号重构方法,并分析该方法的计算复杂度和估计误差的理论极限;最后,采用南海和太平洋海域海表温度数据对方法的有效性进行了评估,结果表明,与现有缺失数据重构方法相比,该文所提LRJS方法有更高的重建精度。
  • 图  1  太平洋海域海表面温度数据采集连接图

    图  2  所有方法在太平洋海域海表面温度数据集上的性能

    图  3  南海海域海表温度数据采集连接图

    图  4  所有方法在南海海域海表温度数据集上的性能

    1  共轭梯度法

     输入:$ {\boldsymbol{Y}},{\boldsymbol{J}},{{\boldsymbol{L}}_{\rm{G}}},{{\boldsymbol{L}}_T},{{\boldsymbol{Z}}^k},{{\boldsymbol{P}}^k},{\boldsymbol{D}},\alpha ,\beta ,\rho $,终止迭代阈值$ \varepsilon $,最
     大迭代次数$ K $
     输出:重构信号时变图信号$ {{\boldsymbol{X}}_{^i}} $
     初始化设置:$ {{\boldsymbol{X}}_i} = 0,\Delta {{\boldsymbol{X}}_i} = 0,i = 0 $
     迭代:
      (1) 确定步长:
        $ \tau = - \dfrac{{\left\langle {\Delta {{\boldsymbol{X}}_i},\nabla f({{\boldsymbol{X}}_i})} \right\rangle }}{{\left\langle {\Delta {{\boldsymbol{X}}_i},\nabla f({{\boldsymbol{X}}_i}) + {\boldsymbol{Y}} + \rho {{\boldsymbol{Z}}_i} - {{\boldsymbol{P}}_i}} \right\rangle }} $
     其中,$ \Delta {{\boldsymbol{X}}_i} $为第$ i $步的搜索方向,$ \tau $为第$ i $步的最优步长,其由线性最小化步长准则$ \mathop {\min }\limits_\tau f({{\boldsymbol{X}}_i} + \tau \Delta {{\boldsymbol{X}}_i}) $决定。
     确定步长:
      (2) 更新搜索方向:
       $ \begin{aligned} & {{\boldsymbol{X}}_{i + 1}} = {{\boldsymbol{X}}_i} + \tau \Delta {{\boldsymbol{X}}_i}; \xi {\text{ = }}\frac{{||\nabla f({{\boldsymbol{X}}_{i + 1}})||_{{\mathrm{F}}} ^2}}{{||\nabla f({{\boldsymbol{X}}_{i + 1}})||_{{\mathrm{F}}} ^2}};\\& \Delta {{\boldsymbol{X}}_{i + 1}} = - \nabla f({{\boldsymbol{X}}_{i + 1}}) + \xi \Delta {{\boldsymbol{X}}_i}\end{aligned}$
     终止条件:如果$ i = K $或者$ {\text{||}}\Delta {{\boldsymbol{X}}_i}|{|_{\mathrm{F}}} \le \varepsilon $,则停止迭代;否则令$ i = i + 1 $,继续迭代,直至满足终止条件。
    下载: 导出CSV

    2  LRJS算法求解步骤

     输入:$ {\boldsymbol{Y}},{\boldsymbol{J}},{{\boldsymbol{L}}_{{\mathrm{G}}} },{{\boldsymbol{L}}_{{{T}}} },{{\boldsymbol{Z}}^k},{{\boldsymbol{P}}^k},{\boldsymbol{D}},\alpha ,\beta ,\rho ,\mu $,终止迭代阈值$ \varepsilon $,
     最大迭代次数$ K $
     输出:重构海表面温度数据$ {{\boldsymbol{X}}^k} $
     初始化设置:$ {{\boldsymbol{X}}^0} = {{\boldsymbol{Z}}^0} = {\boldsymbol{Y}},{{\boldsymbol{P}}^0} = 0,k = 0 $
     迭代:
     (1) 更新${{\boldsymbol{X}}^{k + 1}}$:利用算法1的共轭梯度法;
     (2) 更新${{\boldsymbol{Z}}^{k + 1}}$:利用式(22);
     (3) 更新${{\boldsymbol{P}}^{k + 1}}$:利用式(17);
     终止条件:如果$ k = K $或者${\text{||}}\Delta {{\boldsymbol{X}}^k}|{|_{{\mathrm{F}}} } \le \varepsilon $,则停止迭代;否则
     令$k = k + 1$,继续迭代,直至满足终止条件。
    下载: 导出CSV
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出版历程
  • 收稿日期:  2024-04-09
  • 修回日期:  2024-10-10
  • 网络出版日期:  2024-10-15

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