低秩和聯(lián)合平滑性約束下的時(shí)變海表面溫度重構(gòu)方法

李姣; 萬騰汶; 邱偉

doi:10.11999/JEIT240253

低秩和聯(lián)合平滑性約束下的時(shí)變海表面溫度重構(gòu)方法

doi: 10.11999/JEIT240253

李姣¹,
萬騰汶¹,
邱偉^2, ,

1.
長(zhǎng)沙理工大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院長(zhǎng)沙 410114
2.
中國(guó)人民解放軍國(guó)防科技大學(xué)氣象海洋學(xué)院長(zhǎng)沙 410073

基金項(xiàng)目: 國(guó)家自然科學(xué)基金(42176197)，湖南省自然科學(xué)基金(2022JJ40461)，湖南省教育廳優(yōu)秀青年項(xiàng)目(21B0301)

詳細(xì)信息

作者簡(jiǎn)介:
李姣：女，副教授，研究方向?yàn)樽顑?yōu)化方法及應(yīng)用、生物分子計(jì)算

萬騰汶：女，碩士生，研究方向?yàn)樽顑?yōu)化方法及應(yīng)用

邱偉：男，副教授，研究方向?yàn)橄∈栊盘?hào)重構(gòu)、海洋信息處理

通訊作者:
邱偉　qiuwei08@nudt.edu.cn

中圖分類號(hào): TN911.7
計(jì)量
- 文章訪問數(shù): 128
- HTML全文瀏覽量: 48
- PDF下載量: 18
- 被引次數(shù): 0
出版歷程
- 收稿日期: 2024-04-09
- 修回日期: 2024-10-10
- 網(wǎng)絡(luò)出版日期: 2024-10-15
- 刊出日期: 2024-11-10

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

LI Jiao¹,
WAN Tengwen¹,
QIU Wei^{2
, ,}

1.
School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114, China
2.
School of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China

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

摘要: 海表面溫度對(duì)于海洋動(dòng)力過程及海氣相互作用等具有重要意義，是海洋環(huán)境關(guān)鍵要素之一。浮標(biāo)是海表面溫度觀測(cè)的常用手段，但由于浮標(biāo)在空間的分布不規(guī)則，浮標(biāo)采集的海表面溫度數(shù)據(jù)也呈現(xiàn)非規(guī)則性。另外，浮標(biāo)在實(shí)際工作中難免存在故障，致使采集的海表面溫度數(shù)據(jù)存在缺失。因此對(duì)存在缺失的非規(guī)則海表面溫度數(shù)據(jù)進(jìn)行重構(gòu)具有重要意義。該文通過將海表面溫度數(shù)據(jù)建立為時(shí)變圖信號(hào)，利用圖信號(hào)處理方法解決海表面溫度缺失數(shù)據(jù)重構(gòu)問題。首先，利用數(shù)據(jù)的低秩性和時(shí)域-圖域聯(lián)合變差特性構(gòu)建海表面溫度重構(gòu)模型；其次，基于交替方向乘子法框架提出一種求解該優(yōu)化模型的基于低秩和聯(lián)合平滑性(LRJS)的時(shí)變圖信號(hào)重構(gòu)方法，并分析該方法的計(jì)算復(fù)雜度和估計(jì)誤差的理論極限；最后，采用南海和太平洋海域海表溫度數(shù)據(jù)對(duì)方法的有效性進(jìn)行了評(píng)估，結(jié)果表明，與現(xiàn)有缺失數(shù)據(jù)重構(gòu)方法相比，該文所提LRJS方法有更高的重建精度。
- 海表面溫度 /
- 時(shí)變圖信號(hào) /
- 信號(hào)重構(gòu) /
- 低秩 /
- 聯(lián)合平滑性
Abstract: Sea surface temperature is one of the key elements of the marine environment, which is of great significance to the marine dynamic process and air-sea interaction. Buoy is a commonly used method of sea surface temperature observation. However, due to the irregular distribution of buoys in space, the sea surface temperature data collected by buoys also show irregularity. In addition, it is inevitable that sometimes the buoy is out of order, so that the sea surface temperature data collected is incomplete. Therefore, it is of great significance to reconstruct the incomplete irregular sea surface temperature data. In this paper, the sea surface temperature data is established as a time-varying graph signal, and the graph signal processing method is used to solve the problem of missing data reconstruction of sea surface temperature. Firstly, the sea surface temperature reconstruction model is constructed by using the low rank data and the joint variation characteristics of time-domain and graph-domain. Secondly, a time-varying graph signal reconstruction method based on Low Rank and Joint Smoothness (LRJS) constraints is proposed to solve the optimization problem by using the framework of alternating direction multiplier method, and the computational complexity and the theoretical limit of the estimation error of the method are analyzed. Finally, the sea surface temperature data of the South China Sea and the Pacific Ocean are used to evaluate the effectiveness of the method. The results show that the LRJS method proposed in this paper can improve the reconstruction accuracy compared with the existing missing data reconstruction methods.
- Sea surface temperature /
- Time-varying graph signal /
- Signal reconstruction /
- Low rank /
- Joint smoothness

HTML全文

圖 1 太平洋海域海表面溫度數(shù)據(jù)采集連接圖

下載: 全尺寸圖片幻燈片

圖 2 所有方法在太平洋海域海表面溫度數(shù)據(jù)集上的性能

下載: 全尺寸圖片幻燈片

圖 3 南海海域海表溫度數(shù)據(jù)采集連接圖

下載: 全尺寸圖片幻燈片

圖 4 所有方法在南海海域海表溫度數(shù)據(jù)集上的性能

下載: 全尺寸圖片幻燈片

1 共軛梯度法

輸入：$ {\boldsymbol{Y}},{\boldsymbol{J}},{{\boldsymbol{L}}_{\rm{G}}},{{\boldsymbol{L}}_T},{{\boldsymbol{Z}}^k},{{\boldsymbol{P}}^k},{\boldsymbol{D}},\alpha ,\beta ,\rho $，終止迭代閾值$ \varepsilon $，最　大迭代次數(shù)$ K $
輸出：重構(gòu)信號(hào)時(shí)變圖信號(hào)$ {{\boldsymbol{X}}_{^i}} $
初始化設(shè)置：$ {{\boldsymbol{X}}_i} = 0,\Delta {{\boldsymbol{X}}_i} = 0,i = 0 $
迭代：
(1) 確定步長(zhǎng)：　　　 $ \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} $為第$ i $步的搜索方向，$ \tau $為第$ i $步的最優(yōu)步長(zhǎng)，其由　線性最小化步長(zhǎng)準(zhǔn)則$ \mathop {\min }\limits_\tau f({{\boldsymbol{X}}_i} + \tau \Delta {{\boldsymbol{X}}_i}) $決定。
確定步長(zhǎng)：
(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}$
終止條件：如果$ i = K $或者$ {\text{\|\|}}\Delta {{\boldsymbol{X}}_i}\|{\|_{\mathrm{F}}} \le \varepsilon $，則停止迭代；否則令$ i = i + 1 $，繼續(xù)迭代，直至滿足終止條件。

下載: 導(dǎo)出CSV

2 LRJS算法求解步驟

輸入：$ {\boldsymbol{Y}},{\boldsymbol{J}},{{\boldsymbol{L}}_{{\mathrm{G}}} },{{\boldsymbol{L}}_{{{T}}} },{{\boldsymbol{Z}}^k},{{\boldsymbol{P}}^k},{\boldsymbol{D}},\alpha ,\beta ,\rho ,\mu $，終止迭代閾值$ \varepsilon $，　最大迭代次數(shù)$ K $
輸出：重構(gòu)海表面溫度數(shù)據(jù)$ {{\boldsymbol{X}}^k} $
初始化設(shè)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的共軛梯度法；
(2) 更新${{\boldsymbol{Z}}^{k + 1}}$：利用式(21)；
(3) 更新${{\boldsymbol{P}}^{k + 1}}$：利用式(17)；
終止條件：如果$ k = K $或者${\text{\|\|}}\Delta {{\boldsymbol{X}}^k}\|{\|_{{\mathrm{F}}} } \le \varepsilon $，則停止迭代；否則　令$k = k + 1$，繼續(xù)迭代，直至滿足終止條件。

下載: 導(dǎo)出CSV

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