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Set-Based Transformer for Atmospheric Compensation in Standoff LWIR Hyperspectral Imaging
Fabian Perez, Nicolas Quintero, Jeferson Acevedo, Hoover Rueda-Chacon
TL;DR
Standoff LWIR atmospheric compensation is difficult because range-diverse paths couple measurements to transmittance, atmospheric radiance, and downwelling illumination, while the problem remains underexplored. The paper introduces a set-based framework that jointly estimates these components from multiple ranges and probes its latent space with a sparse autoencoder. Experiments on a MODTRAN-generated dataset report low spectral distortion across the estimated products and geographically coherent activation patterns in several latent features.
Problem
Standoff LWIR compensation remains comparatively underexplored because near-horizontal, range-diverse paths make radiative terms strongly geometry-dependent.
Method
A set-based deep learning framework jointly estimates transmittance, atmospheric path radiance, and shared downwelling radiance from multiple range-diverse measurements, with a sparse autoencoder probing latent representations.
Results
The model achieves low spectral distortion across all atmospheric compensation products, with particularly strong agreement for transmittance.
Takeaways & Limitations
Sparse autoencoder analysis reveals latent features activating on geographically coherent test-data subsets despite no explicit location supervision.
Abstract
from arXiv · showhide
Passive long-wave infrared (LWIR) hyperspectral imaging under a standoff geometry depends on atmospheric absorption and emission, as well as reflected radiance, thus making atmospheric compensation essential to get knowledge of a target of interest. Despite its importance, this compensation has been largely overlooked due to its practical and modeling difficulty. In this paper, we present a lightweight set-based deep learning framework that takes multiple radiance measurements, collected at different standoff ranges, as input and jointly estimates transmittance, atmospheric path radiance, and a shared downwelling spectrum. We analyze the learned representation with a sparse autoencoder and observe that several latent features do activate on geographically coherent subsets of the test data despite the absence of location supervision. Experiments on a MODTRAN generated standoff LWIR dataset demonstrate low spectral distortion across all estimated products. The dataset and code is publicly available at: https://factral.co/SAE-LWIR/
I. INTRODUCTION
Standoff LWIR radiance combines target emission, reflected downwelling irradiance, and atmospheric path emission, with effects varying across range. The paper addresses the resulting need for joint atmospheric compensation using multiple range-diverse measurements.
- LWIR senses thermally emitted radiation in the 8–14 µm atmospheric window, enabling operation independent of solar illumination.
- Standoff measurements are affected by path transmittance, atmospheric upwelling, and surface reflection driven by downwelling irradiance.
- Atmospheric effects vary with standoff range, so compensation requires estimating transmittance, upwelling, and downwelling components.
- Existing approaches largely target airborne or satellite sensing, while standoff LWIR remains comparatively underexplored and some methods omit LWIR or reflected downwelling terms.
- The paper proposes a set-based framework that jointly processes unordered measurements from different standoff ranges to estimate transmittance, upwelling radiance, and shared downwelling radiance.
- The work contributes a publicly available MODTRAN-generated dataset for atmospheric compensation in standoff LWIR imaging.
II. PROPOSED METHOD
The proposed method processes multiple standoff hyperspectral measurements as a set and uses an encoder-decoder architecture to predict atmospheric compensation products. A sparse autoencoder is then used to expose structure in the learned latent representations.
- Each input contains N spectra acquired at different standoff ranges, with each spectrum represented over B spectral bands.
A. Set-based Neural Network
The set-based network processes unordered radiance measurements from multiple standoff ranges and jointly estimates range-dependent transmittance and upwelling radiance alongside shared downwelling radiance. Its architecture enforces permutation equivariance for range-wise outputs and permutation invariance for the shared downwelling estimate.
- Set-based input: The network takes N radiance spectra acquired at different standoff ranges as an unordered input set.Each measurement is represented over B spectral bands.
- Estimated products: It predicts range-wise transmittance and upwelling radiance together with a shared downwelling spectrum.The three outputs are trained against corresponding ground-truth targets.
- Symmetry requirements: Range-wise outputs remain aligned with their inputs under permutation, requiring permutation-equivariant branches.The stated symmetry is GT(P · X) = P · GT(X) and GU(P · X) = P · GU(X).
- Set encoder and decoders: Two stacked induced set-attention blocks form the encoder, whose outputs feed token-wise transmittance and upwelling decoders.The token-wise feedforward networks share structure but not weights across tasks, and applying them to every token preserves permutation equivariance.
- Downwelling decoder: The shared downwelling estimate is produced through attention pooling of the latent tokens into a single vector.The architecture assumes downwelling is common across measurements acquired under the same atmosphere and uses one learned seed vector.
- Training objective: The training objective combines the transmittance, upwelling, and downwelling losses into one total objective.The losses are defined between predicted atmospheric products and their corresponding targets.
B. Sparse Autoencoder (SAE)
The sparse autoencoder probes frozen set-encoder token activations using a sparse overcomplete representation. TopK gating produces sparse features, and a linear dictionary reconstructs the original token activation with an ℓ2 loss.
- SAE inputs: The SAE is trained on frozen encoder outputs, treating each token activation as an independent vector to reconstruct.For an input set X, the encoder produces Z2, and each token zn is used as an activation vector.
- Sparse encoding: TopK gating retains only the K largest-magnitude feature activations and sets the rest to zero.This produces a sparse feature representation from each token activation.
- Reconstruction: A linear dictionary decodes the sparse features back into the token activation.The reconstruction is optimized using a per-token ℓ2 reconstruction loss.
III. DATASET GENERATION
The authors generate a large-scale simulated standoff LWIR atmospheric-compensation dataset using CSP atmospheric profiles and MODTRAN5 radiative-transfer calculations. The resulting dataset spans multiple atmospheric profiles, ranges, and temperatures, with predefined training, validation, and test splits.
- The dataset uses 82,828 CSP atmospheric profiles containing atmospheric state variables such as latitude, longitude, pressure, temperature, humidity, and ozone.
- MODTRAN5 computes band-integrated at-sensor radiance and atmospheric products, using a fixed 45° viewing angle for approximated hemispherical downwelling radiance.
- The simulation uses N = 7 ranges, R = {30, 90, 150, 210, 270, 330, 390} m, with transmittance and atmospheric path radiance computed along each line of sight.
- The generated dataset contains 36,547 profiles, 7 ranges, and 7 temperatures, yielding 255,829 samples.
- The data are randomly split into 70% training, 10% validation, and 20% testing subsets.
IV. RESULTS AND ANALYSIS
Experiments evaluate the framework on simulated standoff LWIR data using single- and multiple-range inputs, alongside qualitative spectral and sparse-autoencoder analyses. The model achieves low distortion across atmospheric-compensation products, while learned features show geographically coherent activation patterns without location supervision.
- Experimental setup: The evaluation uses N = 1 at 270 m and N = 7 measurements per sample, with B = 256 spectral bands over the 8–13 µm window.
- Quantitative and qualitative results: Figure 4 compares predicted and ground-truth transmittance, atmospheric path radiance, and downwelling radiance across the LWIR spectral window.
- Set-size analysis: Increasing the set size from N = 1 to N = 7 provides more range-diverse constraints for the inherently ill-posed estimation problem.
- Quantitative and qualitative results: The model achieves low spectral distortion across all atmospheric-compensation products, with particularly strong agreement for transmittance.
- Quantitative and qualitative results: The plotted spectra preserve fine-grained spectral structure across the estimated products.
- SAE analysis: Several sparse-autoencoder features activate on geographically similar radiance sets, forming location-related clusters despite no explicit location input.
V. CONCLUSIONS
The paper presents a set-based framework for estimating atmospheric-compensation products from range-diverse standoff LWIR measurements and uses sparse autoencoders to probe learned representations.
- The framework estimates transmittance, atmospheric path radiance, and shared downwelling radiance from range-diverse measurements.
- Sparse autoencoders provide an interpretability tool for probing physically grounded representations.