Analysis of Different Noise Reduction Effects of Ground Penetrating Radar Image of Cavity Behind Tunnel Primary Support Based on Singular Value Decomposition and Wavelet Transform

Abstract

The cavity behind the lining structure is a typical disease in tunnel engineering. Cavity seriously affects the interaction between lining and surrounding rock, resulting in uneven bearing of lining structure and stress concentration, which can easily induce lining concrete cracking, water leakage and other diseases. Accurate identification of lining structure cavities is the key to ensure the normal operation of the tunnel. However, the ground penetrating radar detection images of lining cavities often contain interference signals such as background noise, which seriously affects the accuracy and clarity of cavity detection. The application effects of wavelet transform and singular value decomposition in image denoising and resolution of tunnel lining cavity ground penetrating radar are studied. Under this background, the model test of regular and irregular cavity detection behind tunnel lining is carried out, in which the irregular cavity is located in the surrounding rock environment of filling soil to simulate the real situation of tunnel. The measured images of lining cavity under different working conditions are obtained, and the image denoising analysis is carried out. The results show that singular value decomposition can effectively suppress noise. The ground penetrating radar image after singular value decomposition denoising is clearer, and the image resolution is effectively improved, thus realizing the accurate identification of cavity diseases behind the primary support of the tunnel.

Introduction

Background and Motivation

With China’s rapid economic development and the complexity of its tunnel engineering projects, undetected cavity defects behind tunnel linings pose serious risks, including structural failure and casualties. Ground Penetrating Radar (GPR) is widely used to detect such subsurface defects due to its high efficiency and accuracy. However, GPR images are often noisy, making them difficult to interpret accurately.

To address this, the study evaluates two clutter suppression and noise reduction methods:

• Wavelet Analysis

• Singular Value Decomposition (SVD)

2. Technical Methods

• Wavelet Analysis:

  • A time-frequency method that decomposes signals into different frequency bands.

  • Allows denoising by thresholding wavelet coefficients and reconstructing the signal.

• Singular Value Decomposition (SVD):

  • A matrix decomposition technique that isolates significant signal components.

  • Removes noise while preserving meaningful reflections in GPR images.

  • Highly effective in retaining clarity and reducing noise, especially when few singular values dominate the signal.

3. Model Detection Test

Two test models were created simulating tunnel linings under Grade IV surrounding rock:

• Model I: Regular cavities (square, triangular, circular) embedded in concrete.

• Model II: Irregular cavities (pentagonal prism and semi-cylindrical) buried in soil backfill behind tunnel lining.

GPR scans were performed using a RIS system (1600 MHz antenna), and noise was artificially introduced (Gaussian noise) for controlled testing.

4. Results and Image Quality Analysis

Three evaluation metrics were used:

• Signal-to-Noise Ratio (SNR)

• Variance

• Roberts Function (for image edge clarity)

• Clarity Enhancement Ratio

Model I – Regular Cavity

• SVD outperformed Wavelet Analysis in all indicators:

  • Highest SNR: 36.5 vs. 35.6

  • Largest clarity improvement: 255% vs. 22.6%

Model II – Irregular Cavities

• Pentagonal Prism Cavity:

  • Wavelet filtering worsened clarity (-29%)

  • SVD improved it by 45%

• Semi-Cylindrical Cavity:

  • Wavelet filtering had a negative impact (-36%)

  • SVD marginally improved clarity (0.15%)

Conclusion

From the analysis of the denoising results of the radar detection image of the lining structure of the model test, it can be seen that the ground penetrating radar image after singular value decomposition denoising has better performance than wavelet analysis in terms of signal-to-noise ratio, variance, and Roberts function sharpness improvement ratio. It fully shows that the singular value decomposition is significantly better than the wavelet analysis method in noise reduction performance. This method has the best clutter suppression effect and the best noise reduction effect in the actual ground penetrating radar image filtering processing.

References

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Copyright

Copyright © 2025 Chao Zhou, Liang Zhang, Sheng Zhang, Shao Xun Wu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.