L1 ⚛ L1-385 ⊙ Testnet

Image Denoising (Gaussian, Poisson, mixed)

Signal Processing · Pixelwise noise removal

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Markdown — human-readable source of truth

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⬇ L1-385.md

# ⚛ L1 Principle — Image Denoising (Gaussian, Poisson, mixed) **ID:** `L1-385` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Signal Processing — *Pixelwise noise removal* > **🎯 Problem class:** identity plus noise · **🧮 Solution space:** 2D image > **📡 Carrier:** photon · **🌫 Noise:** gaussian or poisson > **⚖ Difficulty (δ):** 2 · **⛓ Block:** 41555197 --- ## 🧠 1. Introduction **Image Denoising (Gaussian, Poisson, mixed)** is a **identity plus noise** whose unknown lives in **2D image** space, within the **Pixelwise noise removal** sub-domain of **Signal Processing**. Measurements consist of photons collected by an optical detector via a **additive noise** sensing mechanism. The forward operator applies one step: pixel-level spatial averaging on the detector. Observations are corrupted by gaussian or poisson. Identity operator with additive noise — trivially well-posed in forward sense; inverse relies on prior (TV, non-local, learned). Mismatch primarily in noise-model specification. ## ⚙ 2. Forward Model Physical chain: **x** → Spatial integration → **y** (detector). ``` y = ∫_A dA x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Signal Processing | | Sub domain | Pixelwise noise removal | | Carrier | photon | | Problem class | identity_plus_noise | | Solution space | 2D_image | | Noise model | gaussian_or_poisson | | Integration axis | none | | Difficulty delta | 2 | | L dag | 1 | ## 📡 4. Measurement Model Identity operator with additive noise — trivially well-posed in forward sense; inverse relies on prior (TV, non-local, learned). Mismatch primarily in noise-model specification. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `gaussian_denoising` · **Forward operator:** `additive_gaussian` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | Sigma n | N | 25 | | Noise type | — | gaussian | | Gain uncertainty | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 64 – 2048 | | W | px | 64 – 2048 | | Sigma n | N | 1 – 75 | | Gain uncertainty | — | 0.0 – 0.3 | | Spatial correlation | — | 0.0 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 30.0 dB PSNR | Metric | Range | |---|---| | Psnr db | 20.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `1` and δ = `2`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xa30aa59dc3132470bf250e77706d21ec57da33e98eef699fc5f5ec631227d7dc` - **Chain tx hash:** `0xb636c7bf47abc44f1caa7b50a860c38caaee1960320e20e23d368796454de699` - **Chain block:** `41555197` --- ## File Mapping This bundle consists of: `L1-385.md`, `L1-385.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-385.md` | Source of truth — edit this | Human or LLM | | `L1-385.json` | Structured metadata for the registry | LLM regenerates from the sections above | **Prompt for your LLM after editing this Markdown:** > Read the attached Markdown. Regenerate the sibling `.json` so every field matches. > Preserve the schema documented in the rows above. > Output each file in its own fenced code block tagged with the filename. > Output only the JSON object. _This Markdown was auto-synthesized from the catalog row for `L1-385`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-385.md).
Regenerate L1-385.json so every field matches the Markdown.
Preserve the schema documented in the File Mapping footer at the bottom of the MD.
Output each file in its own fenced code block tagged with the filename.

⌥ Hierarchy

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L2-385-001 Image Denoising Blind-Noise Spec (SIDD / DND benchmark family)

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📋 JSON metadata

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  "chain_block": 41555197,
  "chain_hash": "0xa30aa59dc3132470bf250e77706d21ec57da33e98eef699fc5f5ec631227d7dc",
  "chain_tx_hash": "0xb636c7bf47abc44f1caa7b50a860c38caaee1960320e20e23d368796454de699",
  "domain": "Signal Processing",
  "hardness_fn": {
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    "kappa": 1,
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    "secondary": "SSIM"
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  "physics_fingerprint": {
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    "difficulty_delta": 2,
    "domain": "Signal Processing",
    "integration_axis": "none",
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    "problem_class": "identity_plus_noise",
    "sensing_mechanism": "additive_noise",
    "solution_space": "2D_image",
    "sub_domain": "Pixelwise noise removal",
    "title": "Image Denoising (Gaussian, Poisson, mixed)"
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  "size_tiers": {
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      "forward_operator": "additive_gaussian",
      "input_format": "measurement_only",
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        "noise_type": "gaussian",
        "sigma_n": 25
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    "epsilon_bounds": {
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      "W": [
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      "gain_uncertainty": [
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      "sigma_n": [
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      "spatial_correlation": [
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        0.5
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    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Pixelwise noise removal",
  "title": "Image Denoising (Gaussian, Poisson, mixed)"
}

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