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:

$$\mathbf{N}(u,\lambda_i) = \mathbf{J}(u,\lambda_i)\,\mathbf{T}(u,\lambda_i) + \mathbf{V}(u,\lambda_i)\left[1-\mathbf{T}(u,\lambda_i)\right]$$

with transmission

$$\mathbf{T}(u,\lambda_i) = \exp[-r\,\alpha(z,\lambda_i)]$$

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

$$\mathbf{J}(u,\lambda_i) = \frac{\mathbf{N}(u,\lambda_i)-\mathbf{V}(u,\lambda_i)}{\mathbf{T}(u,\lambda_i)} + \mathbf{V}(u,\lambda_i)$$

Thus, accurate estimation of $V(u,\lambda_i)$ and $T(u,\lambda_i)$ 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:

• $G_d$ (diffuse-reflectance generator): Estimates diffuse reflectance component from RGB satellite input.
• $G_s$ (specular-reflectance generator): Estimates specular reflectance component.
• $G_t$ (transmission/depth generator): Predicts per-pixel transmission map, representing attenuation due to water depth.
• $G_j$ (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. $G_d$ and $G_s$ take the same RGB+mask inputs—each outputs $\hat{n}_d$ and $\hat{n}_s$ (diffuse/specular).
2. $G_t$ outputs the transmission/depth map $\hat{t}$.
3. $G_j$ receives the sum $\hat{r} = \hat{n}_d + \hat{n}_s$ and transmission $\hat{t}$ (plus a Grey-World estimate for veiling) and outputs the dewatered RGB $\hat{y}$.

3. Loss Functions and Joint Objective

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

• Adversarial loss (cGAN):

$$\mathcal{L}_{cGAN} = \mathbb{E}_{x,y}[\log D(x,y)] + \mathbb{E}_{x}[\log(1-D(x,G_j(\hat{y}_r,\hat{t})))]$$

• Dichromatic model-based reflectance decomposition:
  • Diffuse: $$\mathcal{L}_{gd} = \|L_{gw}(\lambda)gS(u,\lambda)-\hat{y}_d\|_1$$
  • Specular: $$\mathcal{L}_{gs} = \|k(u)L_{gw}(\lambda)-\hat{y}_s\|_1$$
  • Full radiance recon.: $\mathcal{L}_r = \|I(u,\lambda)-(G_d(x)+G_s(x))\|_2$ (water-masked)
• Transmission/depth regularization:
  • $L_1$ transmission: $\mathcal{L}_{t_1} = \|T(u,\lambda)-\hat{y}_t\|_1$
  • Scale-invariant smoothness: $$\mathcal{L}_{t_2} = \frac{1}{n}\sum_i |\nabla_x\log\hat{y}_{t,i}| + |\nabla_y\log\hat{y}_{t,i}|$$
• Radiance-restoration loss: $L_1$ penalty on in-air RGB estimate, masked to water pixels: $\mathcal{L}_{gj}$
• UIFM consistency ("pseudo-reprojection"):

$$\mathcal{L}_N = \|N(u,\lambda)-\hat{N}(u,\lambda)\|_1,\;\;\; \hat{N}=\hat{y}_j\,\hat{t}+V_{gw}(1-\hat{t})$$

These loss terms are combined as:

$$\begin{aligned} \mathcal{L}_{obj} &= \min_{G_d,G_s,G_t,G_j} \max_{D} \;\mathcal{L}_{cGAN} +\gamma\,(\mathcal{L}_{gd}+\mathcal{L}_{gs}) +\sigma\,\mathcal{L}_r +\iota\,\mathcal{L}_{gj} +\tau\,(\mathcal{L}_{t_1}+\mathcal{L}_{t_2}) +\nu\,\mathcal{L}_N\ &\text{with }\gamma=30,\;\sigma=90,\;\iota=100,\;\tau=50,\;\nu=10 \end{aligned}$$

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 ($\approx$98,000 image slices).
• All images (input/output) normalized to $[0,1]$ and resized to $256\times256$.
• 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 $2 \times 10^{-4}$, Adam optimizer with $\beta_1=0.5,\;\beta_2=0.999$.
• Initialization: Generator encoders from ResNet-50 pretrained on ImageNet, with $G_j$ and $G_t$ warm-started from a scene-depth model [González-Sabbagh et al., 2025].
• Input/output sizes: All nets work on $3\times256\times256$ images (except $G_t$ output $1\times256\times256$).
• 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).