High-resolution sub-canopy topography mapping via TanDEM-X DEM combined with future P-band BIOMASS PolInSAR data

Abstract

Precise DEMs at high spatial resolution are indispensable for a variety of scientific studies and applications. Presently, the TanDEM-X mission possesses the capability to collect global-scale InSAR data at high spatial resolution, enabling the generation of a high-resolution global DEM (12 m). Nevertheless, directly utilizing InSAR data poses challenges in detecting sub-canopy topography within forest areas, due to the presence of volume scattering and limited penetration of X-band. Conversely, the upcoming BIOMASS mission operated in P-band will provide an exceptional opportunity for sub-canopy topography extraction, owing to its strong penetration and the capability to collect fully-polarimetric SAR data. However, it is imperative to acknowledge that BIOMASS data do have its own limitation, manifesting as lower resolution (100 m) due to limited bandwidth. To address these challenges and generate high-resolution sub-canopy topography, we propose a new method that leverages the strengths of both TanDEM-X InSAR and BIOMASS PolInSAR datasets through the wavelet transform. We evaluated the performance of our method at two test sites characterized by different forest types and terrain conditions using airborne LiDAR data. Our findings demonstrate a significant improvement in sub-canopy topography accuracy. Specifically, under the boreal coniferous forest scenario, the root mean square error (RMSE) of the resulting sub-canopy topography decreased by 44% compared to the TanDEM-X InSAR DEM. In tropical broadleaf forest scenario, the RMSE reduction reached 64% over the TanDEM-X InSAR DEM. These results indicate the potential of our approach for high-resolution sub-canopy topography mapping by combing data from these two different spaceborne SAR sensors.

Appendix A

In essence, multi-resolution analysis based on the Haar wavelet function can be regarded as a series of averaging and differencing operations applied to a discrete function (Mallat 1989). The high-pass filter has a corresponding impulse response of $\left[ 1/ {\sqrt 2 }\;\;\; -1/ {\sqrt 2 } \right]$, while the low-pass filter has an impulse response of $\left[ 1/ {\sqrt 2 }\;\;\; 1/ {\sqrt 2 } \right]$. When these filters are applied in 2-D dataset, they yield one low-frequency component characterized by long wavelength and three high-frequency components characterized by short wavelengths at each discrete wavelet decomposition level. As an illustrative example, the elevation value (in m) for each pixel is depicted in Fig. 

Fig. 18

Mathematical expression of wavelet low-frequency component sub-band acquisition: a DEM at the original resolution, b one-level wavelet decomposition, and c two-level wavelet decomposition

18a. When performing two low-pass filter operations in both the row and column dimensions at each decomposition level, the resulting low-frequency coefficient can be expressed as follows (e.g. at level = 1, as show in Fig. 18b):

$$ \begin{aligned} {\text{a1}} & = \left[ {\frac{1}{\sqrt 2 }\;\;\frac{1}{\sqrt 2 }} \right] \cdot \left( {\left[ \begin{gathered} a\;b \hfill \\ c\;d \hfill \\ \end{gathered} \right] \cdot \left[ \begin{gathered} \frac{1}{\sqrt 2 } \hfill \\ \frac{1}{\sqrt 2 } \hfill \\ \end{gathered} \right]} \right) \\ & = \frac{1}{2}\left( {a + b + c + d} \right) \\ \end{aligned} $$

(12)

Based on Eq. (12), it becomes evident that each low-frequency coefficient signifies a local weighted average of pixels represented by a, b, c and d. This procedure can be iterated across various scales, enabling the extraction of low-frequency information at the chosen decomposition level, as depicted in Fig. 18c.

Based on the analysis provided above, it is apparent that that each low-frequency coefficient at the decomposition level of $i$ can become $2^{i}$ times the mean of the original elevation, and the spatial resolution can also decrease by a factor of $2^{i}$ times compared to the initial DEM resolution due to the down-sampling operation in the discrete wavelet transform. When applying this processing to the TanDEM-X InSAR DEM, the resultant low-frequency component contains a combination of ground and forest height signals, while the high-frequency components capture terrain details. Additionally, if we do not consider the scaling factor $2^{i}$, the low-frequency part essentially represents a downscaled DEM. To correct the forest influence and obtain accurate ground-level elevation, it is necessary to replace the low-frequency component of the TanDEM-X InSAR DEM with a coarse-resolution ground-level elevation. Thus, it is feasible to produce the sub-canopy topography at a higher resolution by combining the TanDEM-X InSAR DEM and an external coarse-resolution sub-canopy topography dataset, such as BIOMASS PolInSAR sub-canopy topography.