REMAC: Martian Asymmetrical Image Compression

• The paper demonstrates REMAC's ability to shift computational load from Mars rovers to Earth decoders, reducing encoder FLOPs by 43.51% and improving rate-distortion performance.
• The framework integrates reference-guided entropy modeling and multi-scale ref-decoding to exploit both intra-image and inter-image redundancies in Martian scenes.
• A latent feature recycling mechanism minimizes onboard processing by selecting optimal reference features, enabling efficient compression under strict bandwidth and compute constraints.

Reference-Based Martian Asymmetrical Image Compression (REMAC) is an image compression framework purpose-built for Martian remote sensing scenarios, where the uplink communication bandwidth is severely constrained and rover computational resources are highly limited. REMAC achieves compression by leveraging both intra-image and inter-image similarities specific to Martian scenes, using a reference-based architecture that shifts computational burden predominantly to the terrestrial (Earth-side) decoder. The approach integrates a reference-guided entropy model, an asymmetrical encoder–decoder structure, and a latent feature recycling strategy to reduce rover-side complexity while enhancing compression rates compared to conventional learned codecs (Ding et al., 26 Jan 2026).

1. Martian Image Compression Problem and Similarity Analysis

REMAC formalizes the Martian compression problem as optimizing a constrained rate-distortion objective: $$\min_{\theta_{E},\,\theta_{D}} \; R\bigl(b|\theta_{E}\bigr)\;+\;\lambda D\bigl(x,\hat x(\theta_{D})\bigr)$$ subject to the Mars-side encoder's FLOPs not exceeding a strict compute budget $C_{\mathrm{Mars}}$. Here, $R$ is the expected bitrate, $D$ the distortion (often MSE), $\lambda$ a Lagrange multiplier, $x$ an input Martian image, $b$ the bitstream, $\hat x$ the reconstructed image, and $E_{\theta_{E}}, D_{\theta_{D}}$ the encoder and decoder networks.

Extensive quantitative analysis motivates the approach:

• Intra-image texture similarity: BM3D denoising reveals PSNR$_{\text{Mars}}$ values surpassing those for Earth images under identical noise, indicating stronger patch self-similarity.
• Inter-image texture similarity: GLCM features yield pairwise $L_2$ distances that are markedly smaller for Martian images, facilitating reference-based strategies.
• Color similarity: CIE LAB a/b channel standard deviations are substantially lower for Martian images (3.00/4.54 vs 8.44/13.95 for Earth), with chrominance clusters more compactly distributed.
• Semantic similarity: VGG16 ReLU-layer embeddings display reduced $L_2$ distances between Martian images.

These empirical findings favor approaches that exploit both intra- and inter-image redundancies in the encoding process.

2. Asymmetrical Encoder–Decoder Architecture and Computational Shifting

The REMAC architecture is strongly asymmetrical, purpose-built to allocate complexity away from the resource-constrained rover encoder to the Earth-side decoder. The Mars-side encoder is characterized by shallow depth, narrow channels, and small-kernel convolutions, tuned to minimize FLOPs. The decoder—operating with minimal resource constraints—employs deep multi-scale modules, large receptive fields, and reference-integration layers.

A summary FLOPs comparison for compressing a $1600 \times 1152$ Martian image is as follows:

Method	Encoder FLOPs (G)
Hyperprior (Ballé)	151.33
Minnen et al.	362.77
Cheng et al.	699.55
WACNN	1297.64
REMAC	395.16

Parameter counts: Mars-side encoder ≈ 0.5M, decoder ≈ 5M.

3. Reference-Guided Entropy Module

REMAC's entropy module incorporates side information from candidate reference images to improve probabilistic latent modeling and reduce required code length. The architecture includes:

• Hyper-analysis $H_z$: Four $3\times 3$ convolutions and GDN, producing side-latent $z$.
• Hyper-entropy ($H_{\mu'}, H_{\sigma'}$): Each has two $3\times 3$ convolutions generating $\mu'$ and $\sigma'$ from $z$.
• Ref-entropy ($T_{\mu''}, T_{\sigma''}$): Each with two $3\times 3$ convolutions yielding $\mu''$, $\sigma''$ from the reference features $y_{\text{ref}}$.
• Concatenation and autoregressive modeling:

$$\mu = [\mu', \mu''], \quad \sigma = [\sigma', \sigma'']$$

followed by slice-wise channel autoregression ($M=6$).

The conditional latent probability is: $$p(\hat y \mid z, y_{\text{ref}}) = \prod_{i=1}^{N} \left( \mathcal{N}(\hat y_i; \mu_i, \sigma_i)*\mathcal{U}(-\tfrac{1}{2}, \tfrac{1}{2}) \right)$$ where feature map concatenation (not attention) is used for efficiency.

4. Multi-Scale Ref-Decoder and Intra-Image Similarity

The decoder synthesizes high-quality reconstructions by explicitly modeling intra-image similarity via deep multi-scale feature extraction:

• Input-decoder $g_{\text{dec, inp}}$: Four up-sampling convolutions + iGDN with $3\times3$ kernels to reconstruct a coarse image $\hat x_{\text{inp}}$.
• Ref-decoder pathway: Adds learned residual $\hat x_{\text{res}}$ using:
  • Multi-scale reference analysis networks $g_{a, \text{ref}}^{(p)}, p=0..3$ (each: three serial $3\times3$ convs + GDN, yielding an effective $7\times7$ receptive field).
  • Reference synthesis $g_{s, \text{ref}}$ and residual synthesis $g_{s, \text{res}}$.
• Residual-Fusion Block (CRB$^\uparrow$): Concatenates $[\hat y; \text{multi-scale ref feats}]$, two $3\times 3$ convs with ReLU, skip-connection, and up-sampling as required.

Reconstruction is expressed as: $$\hat x = g_{\text{dec, inp}}(\hat y) + g_{s, \text{res}}\bigl(\hat y, \{g_{a, \text{ref}}^{(p)}(x_{\text{ref}})\}\bigr)$$

5. Latent Feature Recycling for Mars-Side Complexity Reduction

To minimize computational overhead during inference, REMAC employs a latent feature recycling mechanism:

• Precompute: For all $N$ reference images, compute $y_{\text{ref}}[n]$ via the full encoder.
• Inference: For each input $x$, compute deep features once, measure $L_1$ distance to all $y_{\text{ref}}[n]$, select best-matching “deep” reference. Only shallow features are recomputed for selected reference and $x$.
• Pseudocode summary:

# Precompute on Mars: for n in 1…N: y_ref[n] ← Encoder_ShallowDeep(x_ref[n]) # During inference: y ← Encoder_ShallowDeep(x) # deep part only once s[n] = ‖y – y_ref[n]‖₁ # deep-feature L1 distance q ← argmin_n s[n] # select “deep” ref j ← pre‐selected shallow ref index y_shallow ← Encoder_Shallow(x) y_ref_shallow ← Encoder_Shallow(x_ref[j]) b ← ReferenceGuidedEntropy([y_shallow, y_ref_shallow, y_ref[q]]) send b → Earth

• Complexity reduction: Encoder GFLOPs decrease from 406.85 to 395.16 ($-$2.87%); overall encoder complexity is reduced by 43.51% versus SOTA.

6. Optimization Objective and Training Regimen

REMAC is trained end-to-end with a rate-distortion (R–D) loss: $$L(\theta, \phi) = R_y + R_z + \lambda D \approx R_y + R_z + \lambda \frac{1}{N}\|x-\hat x\|_2^2$$ Where: $$R_y = \mathbb{E}_{\hat y}\left[-\log p(\hat y \mid z, y_{\text{ref}})\right], \quad R_z = \mathbb{E}_{\hat z}[-\log p(\hat z)]$$ No auxiliary or adversarial losses are used.

7. Empirical Results and Comparative Performance

Experiments are carried out on the MIC dataset (3,088 Martian images: 2,702 train, 386 reference), using $512\times512$ patches and eight $\lambda$ settings for variable bitrate. Evaluation metrics include PSNR, MS-SSIM (dB scale), LPIPS, and their BD (Bjøntegaard Delta) variants.

Method	Encoder FLOPs (G)	BD-PSNR (dB)
Cheng et al.	699.55	+0.6830
REMAC	395.16	+0.9494
Reduction and Gain	–43.51%	+0.2664 dB

REMAC demonstrates substantial Mars-side complexity reduction and superior rate-distortion performance against symmetric learned codecs.

8. Conclusions and Prospective Extensions

REMAC systematically exploits intrinsic similarities in Martian imaging through reference-guided entropy modeling and deep multi-scale ref-decoding, achieving a marked shift of computational effort from the rover to ground-side processing. The latent feature recycling mechanism further streamlines Mars-side operations, enabling deployment in severely resource-constrained environments (e.g., 256 MB DRAM).

Planned extensions include decoder-side model compression (quantization, pruning), adaptation to other homogeneous remote sensing domains (e.g., lunar, underwater), and integration of advanced attention modules within the entropy model to sharpen conditional probabilities (Ding et al., 26 Jan 2026).