Small dataset PSInSAR surface deformation estimation method based on improved low-rank tensor decomposition

doi:10.7523/j.ucas.2024.044

Abstract

Abstract:

In addressing the issue of inadequate precision in surface deformation estimation using the PSInSAR technique with small datasets， this study proposes a dual-weighted low-rank tensor decomposition algorithm for denoising the observed data of temporal interferometric phases. This algorithm enhances the applicability of tensor decomposition in the context of small dataset PSInSAR technology， particularly in larger urban areas. This article utilizes a dataset comprising 29 TerraSAR images from the Tianjin region and extracts a subset of 6 to 11 images as a small dataset for validating the proposed algorithm. The combined approach of dual-weighted tensor decomposition and PSInSAR is employed for ground subsidence estimation. Experimental results demonstrate a significant improvement in the quality of surface deformation estimation using the proposed algorithm for small dataset PSInSAR technology. In the region exhibiting detailed deformation under the condition of 11 images， the error in deformation rate estimation is reduced by approximately 82% compared to the results obtained using the original low-rank tensor decomposition algorithm with the same number of SAR images.

Key words: PSInSAR, small datasets, low rank tensor decomposition, ground settlement

CLC Number:

P237

Xiaoyu LI, Jili WANG, Lu LI, Shiqiang LI. Small dataset PSInSAR surface deformation estimation method based on improved low-rank tensor decomposition[J]. Journal of University of Chinese Academy of Sciences, 2026, 43(3): 414-421.

Figures/Tables 10

Fig.1 Example of temporal interferometric phase tensor

Table 1 Dual-weighted low-rank tensor decomposition approach

输入：观测张量

G

，初始权值

w d, n

，

w L, n

，

W E

，参数

γ, μ, ε 1

1.子问题 $X$ ： $X k + 1 = a r g m i n X L (X, E k, Y k)$

2.子问题 $E$ ： $E k + 1 = a r g m i n E L (X k + 1, E, Y k)$

3.子问题 $Y$ ： $Y k + 1 = Y k - μ (X k + 1 + E k + 1 - G)$

4.更新变量 $w d, n$ ， $w L, n$ ， $W E$ ：

$w d, 1 k + 1 (r 1 : p 1) = σ r 1 (X (1) k + 1) σ (X (1) k + 1) (r 1 : p 1)$

$w d, 2 k + 1 (r 2 : p 2) = σ r 2 (X (2) k + 1) σ (X (2) k + 1) (r 2 : p 2)$

$w L, n k + 1 = 1 σ (X (n) k + 1) + ε$ ， $W E k + 1 = 1 E k + 1 + ε$

5.判断是否满足收敛条件

输出：

X ̂

，

E ̂

Table 1 Dual-weighted low-rank tensor decomposition approach

输入：观测张量

G

，初始权值

w d, n

，

w L, n

，

W E

，参数

γ, μ, ε 1

1.子问题 $X$ ： $X k + 1 = a r g m i n X L (X, E k, Y k)$

2.子问题 $E$ ： $E k + 1 = a r g m i n E L (X k + 1, E, Y k)$

3.子问题 $Y$ ： $Y k + 1 = Y k - μ (X k + 1 + E k + 1 - G)$

4.更新变量 $w d, n$ ， $w L, n$ ， $W E$ ：

$w d, 1 k + 1 (r 1 : p 1) = σ r 1 (X (1) k + 1) σ (X (1) k + 1) (r 1 : p 1)$

$w d, 2 k + 1 (r 2 : p 2) = σ r 2 (X (2) k + 1) σ (X (2) k + 1) (r 2 : p 2)$

$w L, n k + 1 = 1 σ (X (n) k + 1) + ε$ ， $W E k + 1 = 1 E k + 1 + ε$

5.判断是否满足收敛条件

输出：

X ̂

，

E ̂

Fig.2 Technical flowchart

Table 2 Parameters of TerraSAR-X images

序号	成像时间	空间基线/m	时间基线/d	序号	成像时间	空间基线/m	时间基线/d
1	2009/03/27	105.431	-176	16	2009/09/30	-116.999	11
2	2009/04/07	131.836	-165	17	2009/10/11	26.349	22
3	2009/04/18	40.758	-154	18	2009/10/22	-0.982	33
4	2009/04/29	76.838	-143	19	2009/11/02	183.128	44
5	2009/05/10	94.545	-132	20	2009/11/13	64.081	55
6	2009/05/21	128.200	-121	21	2009/11/24	110.749	66
7	2009/06/01	106.172	-110	22	2009/12/05	190.391	77
8	2009/06/23	-12.333	-88	23	2009/12/16	186.009	88
9	2009/07/04	46.593	-77	24	2009/12/27	197.184	99
10	2009/07/15	31.428	-66	25	2010/01/07	40.110	110
11	2009/07/26	-47.821	-55	26	2010/01/18	37.684	121
12	2009/08/06	201.396	-44	27	2010/01/29	56.600	132
13	2009/08/28	-36.912	-22	28	2010/02/20	-89.664	154
14	2009/09/08	101.334	-11	29	2010/03/03	-86.202	165
15	2009/09/19	0	0

Fig.3 PS distribution and deformation rate map

Fig.4 Distribution of spatial and temporal baselines

Fig.5 Results of deformation rate obtained by different algorithms

Fig.6 Deformation rate estimation of different algorithms at the profile location marked in Fig 5

Table 3 MAE between deformation estimation values and reference values for different algorithms

算法	PSI	PSI+RoMIO	PSI+双加权RoMIO
MAE/（mm/a）	14.0	15.8	2.8

Table 4 MAE of deformation estimation values and reference values for different small datasets

影像数量	10	9	8	7	6
MAE/（mm/a）	3.8	3.3	5.3	5.5	7.1

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