DichroGAN: Seafloor Color Restoration cGAN

• DichroGAN is a conditional generative adversarial network that restores true, dewatered seafloor colors by compensating for depth-dependent spectral distortions.
• The architecture integrates four specialized generators with a U-Net style encoder–decoder and a ViT-based discriminator to disentangle diffuse, specular, and transmission components.
• Quantitative evaluations demonstrate superior SSIM and PSNR compared to state-of-the-art methods, highlighting its potential for robust underwater image reconstruction.

DichroGAN is a conditional generative adversarial network (cGAN) designed for the restoration of true in-air seafloor colors from satellite imagery, effectively compensating for the severe, depth-dependent spectral distortions imposed by the water column. The methodology integrates a physically motivated underwater image formation equation with a four-generator architecture, explicitly disentangling diffuse and specular reflectance, transmission, and veiling light, to produce accurate "dewatered" (in-air) radiance estimates. DichroGAN is trained and validated on PRISMA satellite hyperspectral data and demonstrates quantitative and qualitative improvements over state-of-the-art underwater image restoration techniques (Gonzalez-Sabbagh et al., 1 Jan 2026).

1. Physical Modeling: Underwater Image Formation

DichroGAN is grounded in a physically explicit model of underwater radiative transfer, primarily using Duntley’s underwater image formation model (UIFM). For each spectral band $\lambda_i$, the observed radiance $N$ is:

$$\begin{aligned} N(z,\theta,\phi,\lambda_i) &= J(z,\theta,\phi,\lambda_i)\,\exp[-\alpha(z,\lambda_i)\,r] \ &+V(z,\theta,\phi,\lambda_i)\,\exp[K(z,\theta,\phi,\lambda_i)\,r\cos\theta] \ &\qquad\times\left\{1-\exp\left[-\alpha(z,\lambda_i)\,r+K(z,\theta,\phi,\lambda_i)\,r\cos\theta\right]\right\} \end{aligned}$$

where:

• $N$: observed radiance at the sensor
• $J$: true object radiance (just above the seafloor)
• $V$: veiling light from water column backscatter
• $\alpha(z,\lambda) = a(z,\lambda) + b(z,\lambda)$: total attenuation (absorption + scattering)
• $K$: diffuse attenuation coefficient
• $r$: range from sensor to seafloor
• $(\theta, \phi)$: viewing angles

Under a nadir view, this equation simplifies (per-pixel) to:

$N$0

with transmission

$N$1

Recovery of the "in-air" color requires inverting this mapping:

$N$2

Thus, accurate estimation of $N$3 and $N$4 is essential to reconstruct seafloor color.

2. Network Architecture and Component Functions

DichroGAN’s architecture comprises four generators and a single discriminator, organized within a unified conditional GAN:

• $N$5 (diffuse-reflectance generator): Estimates diffuse reflectance component from RGB satellite input.
• $N$6 (specular-reflectance generator): Estimates specular reflectance component.
• $N$7 (transmission/depth generator): Predicts per-pixel transmission map, representing attenuation due to water depth.
• $N$8 (radiance-restoration generator): Synthesizes the final "dewatered" in-air RGB output, combining the preceding estimations.

All generators utilize a U-Net style encoder–decoder structure:

• Encoder: ResNet-50 pretrained on ImageNet
• Decoder: Five upsampling blocks (feature map sizes: [256, 128, 64, 32, 16])
• Skip connections between encoder and decoder layers

The discriminator is a Vision Transformer (ViT)-based patch-level classifier that evaluates (input, output) pairs for adversarial training.

The comprehensive workflow is as follows:

1. $N$9 and $$\begin{aligned} N(z,\theta,\phi,\lambda_i) &= J(z,\theta,\phi,\lambda_i)\,\exp[-\alpha(z,\lambda_i)\,r] \ &+V(z,\theta,\phi,\lambda_i)\,\exp[K(z,\theta,\phi,\lambda_i)\,r\cos\theta] \ &\qquad\times\left\{1-\exp\left[-\alpha(z,\lambda_i)\,r+K(z,\theta,\phi,\lambda_i)\,r\cos\theta\right]\right\} \end{aligned}$$0 take the same RGB+mask inputs—each outputs $$\begin{aligned} N(z,\theta,\phi,\lambda_i) &= J(z,\theta,\phi,\lambda_i)\,\exp[-\alpha(z,\lambda_i)\,r] \ &+V(z,\theta,\phi,\lambda_i)\,\exp[K(z,\theta,\phi,\lambda_i)\,r\cos\theta] \ &\qquad\times\left\{1-\exp\left[-\alpha(z,\lambda_i)\,r+K(z,\theta,\phi,\lambda_i)\,r\cos\theta\right]\right\} \end{aligned}$$1 and $$\begin{aligned} N(z,\theta,\phi,\lambda_i) &= J(z,\theta,\phi,\lambda_i)\,\exp[-\alpha(z,\lambda_i)\,r] \ &+V(z,\theta,\phi,\lambda_i)\,\exp[K(z,\theta,\phi,\lambda_i)\,r\cos\theta] \ &\qquad\times\left\{1-\exp\left[-\alpha(z,\lambda_i)\,r+K(z,\theta,\phi,\lambda_i)\,r\cos\theta\right]\right\} \end{aligned}$$2 (diffuse/specular).
2. $$\begin{aligned} N(z,\theta,\phi,\lambda_i) &= J(z,\theta,\phi,\lambda_i)\,\exp[-\alpha(z,\lambda_i)\,r] \ &+V(z,\theta,\phi,\lambda_i)\,\exp[K(z,\theta,\phi,\lambda_i)\,r\cos\theta] \ &\qquad\times\left\{1-\exp\left[-\alpha(z,\lambda_i)\,r+K(z,\theta,\phi,\lambda_i)\,r\cos\theta\right]\right\} \end{aligned}$$3 outputs the transmission/depth map $$\begin{aligned} N(z,\theta,\phi,\lambda_i) &= J(z,\theta,\phi,\lambda_i)\,\exp[-\alpha(z,\lambda_i)\,r] \ &+V(z,\theta,\phi,\lambda_i)\,\exp[K(z,\theta,\phi,\lambda_i)\,r\cos\theta] \ &\qquad\times\left\{1-\exp\left[-\alpha(z,\lambda_i)\,r+K(z,\theta,\phi,\lambda_i)\,r\cos\theta\right]\right\} \end{aligned}$$4.
3. $$\begin{aligned} N(z,\theta,\phi,\lambda_i) &= J(z,\theta,\phi,\lambda_i)\,\exp[-\alpha(z,\lambda_i)\,r] \ &+V(z,\theta,\phi,\lambda_i)\,\exp[K(z,\theta,\phi,\lambda_i)\,r\cos\theta] \ &\qquad\times\left\{1-\exp\left[-\alpha(z,\lambda_i)\,r+K(z,\theta,\phi,\lambda_i)\,r\cos\theta\right]\right\} \end{aligned}$$5 receives the sum $$\begin{aligned} N(z,\theta,\phi,\lambda_i) &= J(z,\theta,\phi,\lambda_i)\,\exp[-\alpha(z,\lambda_i)\,r] \ &+V(z,\theta,\phi,\lambda_i)\,\exp[K(z,\theta,\phi,\lambda_i)\,r\cos\theta] \ &\qquad\times\left\{1-\exp\left[-\alpha(z,\lambda_i)\,r+K(z,\theta,\phi,\lambda_i)\,r\cos\theta\right]\right\} \end{aligned}$$6 and transmission $$\begin{aligned} N(z,\theta,\phi,\lambda_i) &= J(z,\theta,\phi,\lambda_i)\,\exp[-\alpha(z,\lambda_i)\,r] \ &+V(z,\theta,\phi,\lambda_i)\,\exp[K(z,\theta,\phi,\lambda_i)\,r\cos\theta] \ &\qquad\times\left\{1-\exp\left[-\alpha(z,\lambda_i)\,r+K(z,\theta,\phi,\lambda_i)\,r\cos\theta\right]\right\} \end{aligned}$$7 (plus a Grey-World estimate for veiling) and outputs the dewatered RGB $$\begin{aligned} N(z,\theta,\phi,\lambda_i) &= J(z,\theta,\phi,\lambda_i)\,\exp[-\alpha(z,\lambda_i)\,r] \ &+V(z,\theta,\phi,\lambda_i)\,\exp[K(z,\theta,\phi,\lambda_i)\,r\cos\theta] \ &\qquad\times\left\{1-\exp\left[-\alpha(z,\lambda_i)\,r+K(z,\theta,\phi,\lambda_i)\,r\cos\theta\right]\right\} \end{aligned}$$8.

3. Loss Functions and Joint Objective

DichroGAN’s training strategy combines adversarial and physically informed losses:

• Adversarial loss (cGAN):

$$\begin{aligned} N(z,\theta,\phi,\lambda_i) &= J(z,\theta,\phi,\lambda_i)\,\exp[-\alpha(z,\lambda_i)\,r] \ &+V(z,\theta,\phi,\lambda_i)\,\exp[K(z,\theta,\phi,\lambda_i)\,r\cos\theta] \ &\qquad\times\left\{1-\exp\left[-\alpha(z,\lambda_i)\,r+K(z,\theta,\phi,\lambda_i)\,r\cos\theta\right]\right\} \end{aligned}$$9

• Dichromatic model-based reflectance decomposition:
  • Diffuse: $N$0
  • Specular: $N$1
  • Full radiance recon.: $N$2 (water-masked)
• Transmission/depth regularization:
  • $N$3 transmission: $N$4
  • Scale-invariant smoothness: $N$5
• Radiance-restoration loss: $N$6 penalty on in-air RGB estimate, masked to water pixels: $N$7
• UIFM consistency ("pseudo-reprojection"):

$N$8

These loss terms are combined as:

$N$9

Losses involving physical or radiometric quantities are only applied within water-masked regions to avoid bias from land/cloud pixels.

4. Dataset Construction and Preprocessing

DichroGAN is trained on data derived from PRISMA Level-2 VNIR hyperspectral cubes, which provide:

• 63 bands spanning 400–1010 nm at 30 m GSD.
• RGB synthesis: bands 33 (R), 45 (G), 56 (B).
• Binary water-vs.-nonwater masks via automatic thresholding on NIR bands.

The training corpus includes:

• 1,570 unique RGB scenes with all 63 spectral bands ($J$098,000 image slices).
• All images (input/output) normalized to $J$1 and resized to $J$2.
• Histogram stretch applied to diffuse/specular outputs for improved dynamic range.
• No explicit geometric or photometric augmentation apart from random seed specification.

5. Quantitative Results and Comparative Analysis

DichroGAN’s performance is ascertained through detailed ablations and benchmarks, summarized as follows:

Model	SSIM	PSNR (dB)
cGANs-baseline	0.593	17.75
cWGAN-2	0.524	17.96
cGANs-G_t	0.582	17.78
cGAN-VGG	0.489	16.34
DichroGAN (proposed)	0.672	18.01

On full-reference NASA EO data, DichroGAN achieves the highest SSIM and PSNR scores among tested architectures.

A comparable pattern holds in benchmark comparisons with classical and modern underwater restoration methods (UDCP, CWR, NU²Net, Phaseformer):

• On NASA EO: DichroGAN achieves SSIM 0.560, PSNR 14.39 dB (highest PSNR).
• On combined PRISMA + NASA EO (no-reference): CCF 18.84, UIQM 2.342, NIQE 5.422 (2nd on CCF/NIQE across methods).
• On HICRD & UIEB (underwater benchmarks): best NIQE, competitive CCF/UIQM.

Qualitative analysis shows DichroGAN restores terrain detail and color without over-enhancement or color cast, in contrast to existing methods that often introduce artifacts or fail to remove water silhouettes.

6. Implementation Details and Limitations

• Framework: PyTorch, running on AMD EPYC 7402P CPU with 60 GB RAM.
• Hyperparameters: Batch size 6, epochs 130, learning rate $J$3, Adam optimizer with $J$4.
• Initialization: Generator encoders from ResNet-50 pretrained on ImageNet, with $J$5 and $J$6 warm-started from a scene-depth model [González-Sabbagh et al., 2025].
• Input/output sizes: All nets work on $J$7 images (except $J$8 output $J$9).
• Masking: All key losses are masked to water pixels.
• Limitations: Tendency for slight blurriness (loss of high-frequency detail), somewhat lower performance on metrics biased toward over-enhancement. Future work includes scaling dataset size, multi-term perceptual/texture losses, and evolving to higher-resolution architectures.

7. Significance, Outlook, and Generalization

DichroGAN enables explicit, physically grounded restoration of in-air radiance from satellite images of the seafloor, integrating the dichromatic reflection model and Duntley’s UIFM into a unified deep generative framework. This architecture achieves state-of-the-art restoration across reference and non-reference benchmarks. A plausible implication is that the explicit disentanglement of reflectance, transmission, and veiling light within a deep learning model is critical to robust underwater image reconstruction, and similar frameworks may be extensible to other remote sensing or atmospheric correction domains (Gonzalez-Sabbagh et al., 1 Jan 2026).