# The Use of Ground Penetrating Radar and Microwave Tomography for the Detection of Decay and Cavities in Tree Trunks

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background

#### 2.1. GPR Principles

#### 2.2. Formulation of the Tomographic Inversion Approach

**L**is the K × ${N}_{p}$ dimensional matrix obtained by discretising the integral operator in Equation (1). Since the matrix

**L**stems from the discretisation of an ill-posed integral equation, the inversion of this matrix is an ill-conditioning problem, which means that the solution is very sensitive to measurement uncertainties and data noise. Hence, the TSVD scheme, as expressed in Equation (3), can be applied as a regularisation scheme in order to obtain a robust and physically meaningful solution:

**L**ordered in a decreasing way, ${\left\{{\mathit{u}}_{n}\right\}}_{n=1}^{Q}$ and ${\left\{{\mathit{v}}_{n}\right\}}_{n=1}^{Q}$ are the sets of the singular vectors in the data and the unknown spaces, respectively. The index H ≤ Q ($Q=\mathrm{min}\left\{K,{N}_{p}\right\}$) defines the “degree of regularisation” of the solution and is set in order to find a trade-off between the accuracy and the spatial resolution on one side (tending to increase H) and the solution stability on the other side (tending to reduce H).

#### 2.3. Data Pre-Processing

## 3. Methodology

#### 3.1. Numerical Simulations

#### 3.2. Real Data Acquisitions

## 4. Results and Discussion

#### 4.1. Numerical Simulations

#### 4.1.1. Circular Softwood Tree

#### 4.1.2. Circular Hardwood Tree

#### 4.1.3. Complex-Shaped Hardwood Tree

#### 4.2. Real Scenario

## 5. Conclusion and Future Research

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Geometry of a tree cross-section with an arbitrary shape. The red circles represent the Ground Penetrating Radar (GPR) measurement points along the outer surface of the bark; the white object is a randomly-positioned target within the cross-section.

**Figure 2.**The circular softwood trunk scenario investigated using Finite-Difference Time-Domain (FDTD) numerical modelling. The starting point of the measurements, taken clockwise, is represented by the red circle.

**Figure 3.**The circular hardwood trunk scenario investigated using FDTD numerical modelling. The starting point of the measurements, taken clockwise, is represented by the red circle.

**Figure 4.**The complex-shaped hardwood trunk scenario investigated using FDTD numerical modelling. The starting point of the measurements, taken clockwise, is represented by the red circle.

**Figure 5.**The oak tree trunk investigated at The Faringdon Centre-Non-Destructive Testing Centre, University of West London (UWL), UK. Measurements were taken counter-clockwise and the red circle denotes the starting point.

**Figure 6.**Radargrams of the simulations for the softwood tree scenario. (

**a**) Raw radargam; (

**b**) processed radargram after the application of the pre-processing stage.

**Figure 7.**Tomographic reconstruction of the softwood scenario with time-gating up to 2 ns. The dashed white circle indicates the actual position of the anomaly. The circles in white solid line along the trunk perimeter represent the positions of the measurement points.

**Figure 8.**Tomographic reconstruction of the softwood scenario with time-gating up to 6 ns. The dashed white circle indicates the actual position of the anomaly. The circles in white solid line along the trunk perimeter represent the positions of the measurement points.

**Figure 9.**Radargrams of the simulations for the circular hardwood tree scenario. (

**a**) Raw radargam; (

**b**) processed radargram after the application of the pre-processing stage.

**Figure 10.**Tomographic reconstruction of the circular hardwood tree scenario with time-gating up to 2 ns. The circles in white solid line along the trunk perimeter represent the positions of the measurement points.

**Figure 11.**Tomographic reconstruction of the circular hardwood tree scenario with time-gating up to 6 ns. The dashed white circle indicates the actual position of the anomaly. The circles in white solid line along the trunk perimeter represent the positions of the measurement points.

**Figure 12.**Radargrams of the simulations for the complex-shaped hardwood tree scenario. (

**a**) Raw radargam; (

**b**) processed radargram after the application of the pre-processing stage.

**Figure 13.**Tomographic reconstruction of the complex-shaped hardwood tree scenario with time-gating up to 2 ns. The dashed white circle indicates the actual position of the anomaly. The circles in white solid line along the trunk perimeter represent the positions of the measurement points.

**Figure 14.**Tomographic reconstruction of the complex-shaped hardwood tree scenario without the application of time-gating. The dashed white circle indicates the actual position of the anomaly. The circles in white solid line along the trunk perimeter represent the positions of the measurement points.

**Figure 15.**Radargrams of the real tree scenario. (

**a**) Raw radargam; (

**b**) processed radargram after the application of the pre-processing stage.

**Figure 16.**Tomographic reconstruction of the real tree scenario. The dashed white circles indicate the actual position of the anomalies. The circles in white solid line along the trunk perimeter represent the positions of the measurement points.

**Table 1.**The extended Debye properties of the tree layers [58].

Tree Section Component | Water Content [%] | ${\mathit{\epsilon}}_{\infty}$ | $\mathsf{\Delta}\mathit{\epsilon}$ | $\mathit{\sigma}$ [W^{−1}m^{−1}] | ${\mathit{t}}_{0}\text{}\left(\mathbf{psec}\right)$ |
---|---|---|---|---|---|

Cambium layer | 70 | 9 | 43 | 1 | 9.23 |

Outer sapwood | 30 | 6.1 | 12.36 | 0.033 | 9.23 |

Inner sapwood | 25 | 5.9 | 9.66 | 0.02 | 9.23 |

Rings | 10 | 5.4 | 3.1 | 0.0083 | 9.23 |

Heartwood | 5 | 5.22 | 1.43 | 0.005 | 9.23 |

Bark | 0 | 5 | 0 | 0 | 9.23 |

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## Share and Cite

**MDPI and ACS Style**

Alani, A.M.; Soldovieri, F.; Catapano, I.; Giannakis, I.; Gennarelli, G.; Lantini, L.; Ludeno, G.; Tosti, F. The Use of Ground Penetrating Radar and Microwave Tomography for the Detection of Decay and Cavities in Tree Trunks. *Remote Sens.* **2019**, *11*, 2073.
https://doi.org/10.3390/rs11182073

**AMA Style**

Alani AM, Soldovieri F, Catapano I, Giannakis I, Gennarelli G, Lantini L, Ludeno G, Tosti F. The Use of Ground Penetrating Radar and Microwave Tomography for the Detection of Decay and Cavities in Tree Trunks. *Remote Sensing*. 2019; 11(18):2073.
https://doi.org/10.3390/rs11182073

**Chicago/Turabian Style**

Alani, Amir M., Francesco Soldovieri, Ilaria Catapano, Iraklis Giannakis, Gianluca Gennarelli, Livia Lantini, Giovanni Ludeno, and Fabio Tosti. 2019. "The Use of Ground Penetrating Radar and Microwave Tomography for the Detection of Decay and Cavities in Tree Trunks" *Remote Sensing* 11, no. 18: 2073.
https://doi.org/10.3390/rs11182073