# Feasibility Study of Neural Networks Interpolation Applied to Synthetic Aperture Radar Deformations

Alexis Renier-Robin, Diego Reale, Thibaud Toullier, Simona Verde, Francesco Soldovieri, Jean Dumoulin

## ► To cite this version:

Alexis Renier-Robin, Diego Reale, Thibaud Toullier, Simona Verde, Francesco Soldovieri, et al., Feasibility Study of Neural Networks Interpolation Applied to Synthetic Aperture Radar Deformations. European Geosciences Union, Apr 2023, Vienne (Autriche), Austria. 10.5194/egusphere-egu23-14562. hal-04797800

HAL Id: hal-04797800

https://inria.hal.science/hal-04797800v1

Submitted on 22 Nov 2024

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Distributed under a Creative Commons Attribution 4.0 International License
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## Context

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* Need to survey a very large number of civil structures that are aging[2] and validate new ones performances

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* Recent technological advances for economical and practical on site monitoring

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* Availability and progress in data acquired by satellite Synthetic Aperture Radar (SAR)

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* Challenge of Structural Health Monitoring (SHM) based on modal parameter analysis has to deal with environmental variations[3]

<figure><img src="image_8.png" /><figcaption>Fig. 1: Imaging geometries of SAR observations over ascending and descending orbits</figcaption></figure>

## DInSAR Peculiarities[1]

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* Robustness of estimated ground deformation by combining the Line-of-sight (LOS) deformation measurements of complementary ascending and descending orbits data, for which the **measurements points and date of acquisition could be different**;

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* Sparse, or absence of, measurements points on some areas induced by strong decorrelation phenomena;

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* Limited range of the actual structure deformation that could reach the accuracy of the DInSAR technology.

## Needs

* Interpolate data on a regular grid to overcome missing points and have the same points for both orbits (spatial)

* Fusion of the different dates for two acquisition trajectories (temporal)

## Dataset and Methodology

### Naples dataset (Italy)

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* Railway with missing observations on ground due to a crossing bridge

### Data processing

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* Extraction of points from AOI

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* Projection, rotation and normalization of the points for inputs to the interpolation

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* Grid generation

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* Projection, rotation and normalization of the grid for inputs to the interpolation

### Interpolation

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* Kriging is a well known spatial interpolation method for providing the best linear unbiased predictor. **But** relies on the fit of a variance model, often optimistic.

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* Interpolation based on DeepKriging[4]

1. A special training grid for the network is created

2. For each acquisition point, the distance to each point of the grid is calculated.

3. The distances are recalculated in a process comparable to an inversion. This modified distance will be the input to the neural network. Thus, for an acquisition point, the closer a point in the training grid is, the greater the input value of the neural network is.

4. The result of the network is the estimated subsidence of each points of the grid.

## Conclusion

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* Development of a processing toolchain applied to DInSAR data for DeepKriging

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* To our knowledge, first Neural Network Interpolation on DInSAR data

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* Results are promising but need to be validated with ground truth experiments

## Perspectives

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* Adjustments in the network could be made to further improve the interpolation

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* Testing the approach on a monitored bridge in Nantes (France)

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* Perform the interpolation on both orbits to combine them

## Objectives

Study the feasibility of using surface deformation measurements from Differential Interferometric SAR (DInSAR) technology to subsidence characterization and quasi-periodic monitoring of civil infrastructures.

Particularly in case of lack of information inherent to the DInSAR satellite measurements.

### Inputs

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* Dataset of subsidence

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* Dataset of shapes for Area-of-interest (AOI)

<figure><img src="image_27.png" /><figcaption>Fig. 2: Workflow of the developed algorithm</figcaption></figure>

## Bibliography

[1] Antonio Pepe and Fabiana Calò. "A Review of Interferometric Synthetic Aperture RADAR (InSAR) Multi-Track Approaches for the Retrieval of Earth's Surface Displacements". In: *Applied Sciences* 7.12 (2017). DOI: 10.3390/app7121264. url: https://www.mdpi.com/2076-3417/7/12/1264.

[2] Riccardo Lanari et al. "Comment on "Pre-Collapse Space Geodetic Observations of Critical Infrastructure: The Morandi Bridge, Genoa, Italy" by Milillo et al. (2019)". In: *Remote Sensing* 12.24 (2020). DOI: 10.3390/rs12244011. url: https://www.mdpi.com/2072-4292/12/24/4011.

[3] Sérgio Pereira, et al., "Dynamic Monitoring of a Cable-Stayed Bridge: Monitoring System and First Results", EWSHM2022, (July 2022), Palermo, Italy.

[4] Wanfang Chen et al. "DeepKriging: Spatially Dependent Deep Neural Networks for Spatial Prediction". In: arXiv:2007.11972 (May 23, 2022). url: http://arxiv.org/abs/2007.11972.

## Results

<figure><img src="image_28.png" /><figcaption>Fig. 3: Interpolated subsidence data, profile view.</figcaption></figure>

<figure><img src="image_29.png" /><figcaption>Fig. 4: Estimated velocity map on the regular grid in mm/year (interpolated)</figcaption></figure>

<figure><img src="image_30.png" /><figcaption>Fig. 5: Comparison of the DeepKriging interpolation (orange) with a linear (blue), nearest (purple) and natural (yellow) interpolations. Original data in green.</figcaption></figure>

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