Global-scale radar data restoration algorithm based on total variation and low-rank group sparsity

doi:10.11772/j.issn.1001-9081.2020122047

Journal of Computer Applications ›› 2021, Vol. 41 ›› Issue (11): 3353-3361.DOI: 10.11772/j.issn.1001-9081.2020122047

• Multimedia computing and computer simulation • Previous Articles Next Articles

Global-scale radar data restoration algorithm based on total variation and low-rank group sparsity

Chenyu GE, Liang DONG, Yikun XU, Yi CHANG, Hongming ZHANG()

College of Information Engineering，Northwest Agriculture and Forestry University，Yangling Shaanxi 712100，China

Received:2020-12-28 Revised:2021-05-14 Accepted:2021-05-19 Online:2021-05-14 Published:2021-11-10
Contact: Hongming ZHANG
About author:GE Chenyu，born in 1995，M. S. candidate. His research interests include machine learning，image restoration
DONG Liang，born in 1998，M. S，candidate. His research interests include spatial big data analysis，digital terrain analysis
XU Yikun，born in 1996，M. S. candidate. His research interests include big data management and analysis，parallel computing
CHANG Yi，born in 1995，M. S. candidate. His research interests include spatial big data analysis，parallel computing
ZHANG Hongming， born in 1979， Ph. D.， professor. His research interests include spatial big data analysis，geographic information system，soil erosion evaluation.
Supported by:
the Surface Program of National Natural Science Foundation of China(41771315);the Key Research and Development Project in Ningxia Hui Autonomous Region(2017BY067);the EU Horizon 2020 Research and Innovation Program （ISQAPER： 635750）

基于总变分低秩组稀疏的全球雷达数据修复算法

葛晨宇, 董良, 许伊昆, 常毅, 张宏鸣()

西北农林科技大学信息工程学院，陕西杨凌712100

通讯作者: 张宏鸣
作者简介:葛晨宇（1995—），男，陕西西安人，硕士研究生，CCF会员，主要研究方向：机器学习、图像复原
董良（1998—），男，陕西汉中人，硕士研究生，CCF会员，主要研究方向：空间大数据分析、数字地形分析
许伊昆（1996—），男，陕西西安人，硕士研究生，主要研究方向：大数据管理分析、并行计算
常毅（1995—），男，陕西榆林人，硕士研究生，CCF会员，主要研究方向：空间大数据分析、并行计算
张宏鸣（1979—），男，内蒙古赤峰人，教授，博士，博士生导师，CCF会员，主要研究方向：空间大数据分析、地理信息系统、土壤侵蚀评价。
基金资助:
国家自然科学基金面上项目(41771315);宁夏回族自治区重点研究开发项目(2017BY067);欧盟地平线2020研究与创新计划项目（ISQAPER：635750）

Abstract

Abstract:

The mixed noise formed by a large number of spikes， speckles and multi-directional stripe errors in Shuttle Radar Terrain Mission （SRTM） will cause serious interference to the subsequent applications. In order to solve the problem， a Low-Rank Group Sparsity_Total Variation （LRGS_TV） algorithm was proposed. Firstly， the uniqueness of the data in the local range low-rank direction was used to regularize the global multi-directional stripe error structure， and the variational idea was used to perform unidirectional constraints. Secondly， the non-local self-similarity of the weighted kernel norm was used to eliminate the random noise， and the Total Variation （TV） regularity was combined to constrain the data gradient， so as to reduce the difference of local range changes. Finally， the low-rank group sparse model was solved by the alternating direction multiplier optimization to ensure the convergence of model. Quantitative evaluation shows that， compared with four algorithms such as TV， Unidirectional Total Variation （UTV）， Low-Rank-based Single-Image Decomposition （LRSID） and Low-Rank Group Sparsity （LRGS） model， the proposed LRGS_TV has the Peak Signal-to-Noise Ratio （PSNR） of 38.53 dB and the Structural SIMilarity （SSIM） of 0.97， which are both better than the comparison algorithms. At the same time， the slope and aspect results show that after LRGS_TV processing， the subsequent applications of the data can be significantly improved. The experimental results show that， the proposed LRGS_TV can repair the original data better while ensuring that the terrain contour features are basically unchanged， and can provide important support to the reliability improvement and subsequent applications of SRTM.

Key words: data restoration, Total Variation (TV), low-rank, group sparsity, terrain factor, Shuttle Radar Terrain Mission (SRTM)

摘要：

针对航天飞机雷达地形测绘任务（SRTM）中存在由大量尖峰、斑点和多向条纹误差形成的混合噪声对后续应用产生严重干扰的问题，提出了一种基于总变分约束的低秩组稀疏（LRGS_TV）算法。首先，利用数据在局部范围低秩方向上的唯一性来正则化全局多方向条带误差结构，同时使用变分思想进行单向约束；其次，使用加权核范数的非局部自相似性来消除随机噪声，并结合总变分（TV）正则对数据梯度进行约束，以减小局部范围变化差值；最后，使用交替方向乘子优化对低秩组稀疏模型进行求解，从而保证了模型的收敛性。把所提算法与TV、单方向总变分（UTV）、低秩单图像分解（LRSID）和低秩组稀疏（LRGS）模型这4种算法进行定量评估的结果表明，LRGS_TV的峰值信噪比（PSNR）可以达到38.53 dB，结构相似性（SSIM）可以达到0.97，均为5种算法中的最优。同时，坡度与坡向结果表明，经LRGS_TV处理后，数据的后续应用有显著改善。实验结果表明，LRGS_TV能够在保证地形轮廓特征基本不变的情况下更好地修复原始数据，可对SRTM可靠性的提高与后续应用提供重要的支持。

关键词: 数据修复, 总变分, 低秩, 组稀疏, 地形因子, 航天飞机雷达地形测绘任务

CLC Number:

TP391.41

Chenyu GE, Liang DONG, Yikun XU, Yi CHANG, Hongming ZHANG. Global-scale radar data restoration algorithm based on total variation and low-rank group sparsity[J]. Journal of Computer Applications, 2021, 41(11): 3353-3361.

葛晨宇, 董良, 许伊昆, 常毅, 张宏鸣. 基于总变分低秩组稀疏的全球雷达数据修复算法[J]. 《计算机应用》唯一官方网站, 2021, 41(11): 3353-3361.

Figures/Tables 10

Fig. 1 Technical roadmap of global-scale radar data restoration algorithm

Fig. 2 SRTM data and experimental sample areas

Fig. 3 Error elimination effect comparison of different algorithms in sample area 1

Tab. 1 PSNR and SSIM evaluation results of different algorithms in different sample areas

算法	样区1		样区2		样区3		样区4
算法	PSNR/dB	SSIM	PSNR/dB	SSIM	PSNR/dB	SSIM	PSNR/dB	SSIM
加入混合噪声	32.45	0.61	26.62	0.79	37.25	0.77	34.90	0.77
TV	33.32	0.69	27.34	0.86	38.30	0.96	35.46	0.85
UTV	32.47	0.59	25.37	0.67	38.08	0.87	35.74	0.88
LRSID	32.91	0.70	26.99	0.83	37.64	0.87	35.38	0.87
LRGS	33.15	0.75	27.57	0.92	38.44	0.95	35.86	0.91
LRGS_TV	33.53	0.86	27.70	0.94	38.53	0.97	35.97	0.96

Fig. 4 Slope results calculated by different algorithms after eliminating data errors in sample area 1

Fig. 5 Cumulative frequency of slope difference

Fig. 6 Aspect results calculated by different algorithms after eliminating data errors in sample area 1

Fig. 7 Error elimination effect comparison of different algorithm in sample area 5

Fig. 8 Results of slope and aspect obtained by LRGS_TV in sample area 5

Tab. 2 Time consumed by different algorithms to restore data under different data sizes

数据规模	不同算法修复数据所消耗的时间
数据规模	TV	UTV	LRSID	LRGS	LRGS_TV
50×50	0.16	0.17	1.30	1.40	1.60
100×100	0.18	0.19	1.53	5.43	5.55
250×250	0.19	0.21	3.26	10.75	11.33
512×512	0.35	0.52	11.93	30.46	31.37
1 000×1 000	0.91	1.50	45.17	105.45	106.63

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Global-scale radar data restoration algorithm based on total variation and low-rank group sparsity

基于总变分低秩组稀疏的全球雷达数据修复算法

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