# A TSVD-Based Method for Forest Height Inversion from Single-Baseline PolInSAR Data

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## Abstract

**:**

## 1. Introduction

## 2. RVoG Model

## 3. The TSVD-Based Method for the Estimation of Vegetation Height From Complex Interferometric Coherence Observations

#### 3.1. Estimation of Pure Volume Coherence from the Complex Interferometric Coherence Observations

#### 3.2. Extraction of Vegetation Height from the Pure Volume Coherence

#### 3.3. The Determination of Initial Values of Model Parameters

## 4. Examples

#### 4.1. Simulated Experiments

#### 4.2. Validation with E-SAR P-Band Data

#### 4.2.1. Study Area and Data Sets

#### 4.2.2. Forest Height Inversion

^{2}) were calculated to validate the performance. The validated stand-level plots are displayed in Figure 7.

^{2}values of 0.2166 and 0.5824, respectively. This indicates that the forest heights inverted by TSVD are closer to the LiDAR forest heights. The RMSEs of the three-stage method and TSVD are 6.6351 and 3.4096, respectively. Clearly, the inversion accuracy of TSVD is higher than that of the three-stage method, showing an improvement of 48.6%. Therefore, it is possible to state that the TSVD-based method can improve the inversion of the forest height in this test site.

## 5. Discussion

#### 5.1. The Extracted Ground Surface Phases by the Three-Stage Method and TSVD

#### 5.2. Effects on Estimation of Phase Height

#### 5.3. Limitations of the TSVD-Based Method

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 3.**(

**a**) forest height inversion result of the three-stage method; and (

**b**) forest height inversion result of the truncated singular value decomposition (TSVD)-based inversion method.

**Figure 6.**(

**a**) inversion results of the three-stage method; (

**b**) inversion results of the TSVD-based method; (

**c**) forest heights derived by light detection and ranging (LiDAR).

**Figure 7.**(

**a**) forest heights estimated by the three-stage method; (

**b**) forest heights estimated by the TSVD-based method.

**Figure 8.**(

**a**) ground surface phase estimated by the three-stage method; (

**b**) ground surface phase estimated by TSVD; (

**c**) the difference between the ground surface phases obtained by the three-stage method and TSVD.

**Figure 9.**(

**a**) the phase heights extracted from the pure volume coherence obtained by the three-stage method; (

**b**) the phase heights extracted from the pure volume coherence obtained by TSVD; (

**c**) the differences between the phase heights obtained by the three-stage method and TSVD.

**Figure 11.**Forest heights extracted by the least-squares method from the pure volume coherence estimated by the three-stage method.

Platform Height (m) | Center Frequency (Hz) | Incidence Angle (D) | Vertical Baseline (m) | Horizontal Baseline (m) | Vertical Wave Number | Ground Phase (D) | Forest Height (m) |
---|---|---|---|---|---|---|---|

3000 | 1.3 G | 45 | 1 | 10 | 0.1154 | 0 | 18 |

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**MDPI and ACS Style**

Lin, D.; Zhu, J.; Fu, H.; Xie, Q.; Zhang, B.
A TSVD-Based Method for Forest Height Inversion from Single-Baseline PolInSAR Data. *Appl. Sci.* **2017**, *7*, 435.
https://doi.org/10.3390/app7050435

**AMA Style**

Lin D, Zhu J, Fu H, Xie Q, Zhang B.
A TSVD-Based Method for Forest Height Inversion from Single-Baseline PolInSAR Data. *Applied Sciences*. 2017; 7(5):435.
https://doi.org/10.3390/app7050435

**Chicago/Turabian Style**

Lin, Dongfang, Jianjun Zhu, Haiqiang Fu, Qinghua Xie, and Bing Zhang.
2017. "A TSVD-Based Method for Forest Height Inversion from Single-Baseline PolInSAR Data" *Applied Sciences* 7, no. 5: 435.
https://doi.org/10.3390/app7050435