L1 ⚛ L1-383 ⊙ Testnet

Image Super-Resolution (single-image)

Signal Processing · Spatial upsampling inverse problem

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⬇ L1-383.md

# ⚛ L1 Principle — Image Super-Resolution (single-image) **ID:** `L1-383` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Signal Processing — *Spatial upsampling inverse problem* > **🎯 Problem class:** linear inverse upsampling · **🧮 Solution space:** 2D image > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555197 --- ## 🧠 1. Introduction **Image Super-Resolution (single-image)** is a **linear inverse upsampling** whose unknown lives in **2D image** space, within the **Spatial upsampling inverse problem** sub-domain of **Signal Processing**. Measurements consist of photons collected by an optical detector via a **decimated imaging** sensing mechanism. The forward operator applies, in order: K · blur · shiftinvariant operator; D · decimate · spatial operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Inherently underdetermined (s^2:1 information loss); uniqueness restored only under image prior (sparse/natural-image manifold). Stability controlled by anti-alias kernel accuracy and noise level. ## ⚙ 2. Forward Model Physical chain: **x** → K · blur · shiftinvariant → D · decimate · spatial → Spatial integration → **y** (detector). ``` y = ∫_A dA `D.decimate.spatial` `K.blur.shiftinvariant` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `K.blur.shiftinvariant` | K · blur · shiftinvariant operator | | `D.decimate.spatial` | D · decimate · spatial operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Signal Processing | | Sub domain | Spatial upsampling inverse problem | | Carrier | photon | | Problem class | linear_inverse_upsampling | | Solution space | 2D_image | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 2.7 | ## 📡 4. Measurement Model Inherently underdetermined (s^2:1 information loss); uniqueness restored only under image prior (sparse/natural-image manifold). Stability controlled by anti-alias kernel accuracy and noise level. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `bicubic_sr` · **Forward operator:** `bicubic_decimate` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | S | — | 4 | | Jpeg q | — | 100 | | Kernel type | — | bicubic | | Noise level | — | 0 | | Sub pixel shift | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 64 – 1024 | | W | px | 64 – 1024 | | S | — | 2 – 8 | | Jpeg q | — | 20 – 100 | | Noise level | — | 0.0 – 0.08 | | Sub pixel shift | — | 0.0 – 1.0 | | Kernel type error | — | 0.0 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 28.0 dB PSNR | Metric | Range | |---|---| | Psnr db | 18.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `5000` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x287d0bfa3073e32e595f405cf56c346936123ad04709157354e9b1cd18defefb` - **Chain tx hash:** `0xc3105d0f3f48c72d2db0eef8265b78e02e25e18fa00eef1e49d6efd36852af18` - **Chain block:** `41555197` --- ## File Mapping This bundle consists of: `L1-383.md`, `L1-383.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-383.md` | Source of truth — edit this | Human or LLM | | `L1-383.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 `L1-383`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-383.md).
Regenerate L1-383.json so every field matches the Markdown.
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Output each file in its own fenced code block tagged with the filename.

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L2-383-001 Image Super-Resolution Real-World Spec (Real-ESRGAN family)

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📋 JSON metadata

{
  "artifact_id": "L1-383",
  "chain_block": 41555197,
  "chain_hash": "0x287d0bfa3073e32e595f405cf56c346936123ad04709157354e9b1cd18defefb",
  "chain_tx_hash": "0xc3105d0f3f48c72d2db0eef8265b78e02e25e18fa00eef1e49d6efd36852af18",
  "domain": "Signal Processing",
  "hardness_fn": {
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    "kappa": 5000,
    "metric": "PSNR_dB",
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      "name": "primary",
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  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Inherently underdetermined (s^2:1 information loss); uniqueness restored only under image prior (sparse/natural-image manifold). Stability controlled by anti-alias kernel accuracy and noise level.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 2.7,
    "carrier": "photon",
    "difficulty_delta": 3,
    "domain": "Signal Processing",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
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    "problem_class": "linear_inverse_upsampling",
    "sensing_mechanism": "decimated_imaging",
    "solution_space": "2D_image",
    "sub_domain": "Spatial upsampling inverse problem",
    "title": "Image Super-Resolution (single-image)"
  },
  "size_tiers": {
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      "forward_operator": "bicubic_decimate",
      "input_format": "measurement_only",
      "omega": {
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        "W": 256,
        "jpeg_q": 100,
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        "noise_level": 0.0,
        "s": 4,
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    "epsilon_bounds": {
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    },
    "omega_bounds": {
      "H": [
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        1024
      ],
      "W": [
        64,
        1024
      ],
      "jpeg_q": [
        20,
        100
      ],
      "kernel_type_error": [
        0.0,
        0.5
      ],
      "noise_level": [
        0.0,
        0.08
      ],
      "s": [
        2,
        8
      ],
      "sub_pixel_shift": [
        0.0,
        1.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Spatial upsampling inverse problem",
  "title": "Image Super-Resolution (single-image)"
}

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