---
title: 'REMAC: Martian Asymmetrical Image Compression'
url: https://www.emergentmind.com/topics/reference-based-martian-asymmetrical-image-compression-remac
type: topic
---

# REMAC: Martian Asymmetrical Image Compression

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 [2601.18547].

## 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:**
  ```python
  # 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 [2601.18547].

Source: https://www.emergentmind.com/topics/reference-based-martian-asymmetrical-image-compression-remac