Better Coherence, Better Height: Fusing Physical Models and Deep Learning for Forest Height Estimation from Interferometric SAR Data

TL;DR

This paper tackles forest height estimation from InSAR by integrating physics-based modeling with deep learning. It introduces CoHNet, a physics-aware end-to-end framework that uses a neural surrogate to replace a non-differentiable physical model and optimizes a DL-predicted volume decorrelation to drive a RVoG-based height inversion, enforced via a physics-informed loss. The approach yields substantial height estimation improvements over the pure physical model (≈50% error reduction) and competes with direct DL methods, while also supplying an optimized decorrelation output that enhances the reliability and interpretability of the results. Practically, CoHNet offers a robust forest height estimator applicable to AfriSAR TanDEM-X LVIS data, with potential downstream benefits for biomass and carbon stock assessment.

Abstract

Estimating forest height from Synthetic Aperture Radar (SAR) images often relies on traditional physical models, which, while interpretable and data-efficient, can struggle with generalization. In contrast, Deep Learning (DL) approaches lack physical insight. To address this, we propose CoHNet - an end-to-end framework that combines the best of both worlds: DL optimized with physics-informed constraints. We leverage a pre-trained neural surrogate model to enforce physical plausibility through a unique training loss. Our experiments show that this approach not only improves forest height estimation accuracy but also produces meaningful features that enhance the reliability of predictions.

Figures (14)

• Figure 1: CoHNet, an end-to-end network that uses interferometric coherence estimated from InSAR data (backscatter of one image shown on the left), derives optimized volume decorrelation (center) which is then leveraged by a physical model to estimate forest height (right). White regions in the maps denote non-forest areas.
• Figure 2: Overview of CoHNet for forest height estimation. The first network estimates the optimized volume decorrelation $\hat{\gamma}_\text{Vol}$ from the given coherence $\gamma$. The loss calculated from the output of the second network (with fixed, pre-trained weights) using this parameter together with the vertical wavenumber $\kappa_z$ compared to a reference forest height is back-propagated through the entire pipeline to update the weights of the first network.
• Figure 3: Performance (RMSE in [m]) of different models trained (rows) and tested (columns) over various regions. The scale of each heatmap is normalized per subplot for better comparison. Subplots represent (a) Pre-trained NSM, (b) CoHNet with Gabon NSM, (c) CoHNet with region-wise NSM, and (d) Direct Model. Each model demonstrates varying degrees of adaptability across dataset regions.
• Figure 4: Qualitative results for CoHNet trained on Gabon over the four regions: Mabounie, Rabi, Pongara, and Lope. Areas with no available LVIS reference are shown in white. Predictions are masked by a forest/non-forest map (white regions denote areas with no forest).
• Figure 5: Qualitative comparison of forest height estimates from different models such as the physical model (RVoG), the direct model, CoHNet, and the difference (CoHNet - Direct Model) for the Mabounie region.