L1 ⚛ L1-382 ⊙ Testnet

Image Deblurring (non-blind and blind deconvolution)

Signal Processing · 2D convolutional deblurring

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⬇ L1-382.md

# ⚛ L1 Principle — Image Deblurring (non-blind and blind deconvolution) **ID:** `L1-382` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Signal Processing — *2D convolutional deblurring* > **🎯 Problem class:** linear inverse deconvolution · **🧮 Solution space:** 2D image > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555196 --- ## 🧠 1. Introduction **Image Deblurring (non-blind and blind deconvolution)** is a **linear inverse deconvolution** whose unknown lives in **2D image** space, within the **2D convolutional deblurring** sub-domain of **Signal Processing**. Measurements consist of photons collected by an optical detector via a **shift invariant blur** sensing mechanism. The forward operator applies, in order: K · blur · shiftinvariant operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Non-blind: deconvolution is ill-conditioned with kappa proportional to |OTF|^-1 at high frequencies; Tikhonov regularization bounds kappa_eff. Blind: bilinear in (k, x) and non-convex; only locally well-posed under sparse-gradient prior. ## ⚙ 2. Forward Model Physical chain: **x** → K · blur · shiftinvariant → Spatial integration → **y** (detector). ``` y = ∫_A dA `K.blur.shiftinvariant` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `K.blur.shiftinvariant` | K · blur · shiftinvariant operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Signal Processing | | Sub domain | 2D convolutional deblurring | | Carrier | photon | | Problem class | linear_inverse_deconvolution | | Solution space | 2D_image | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 2 | ## 📡 4. Measurement Model Non-blind: deconvolution is ill-conditioned with kappa proportional to |OTF|^-1 at high frequencies; Tikhonov regularization bounds kappa_eff. Blind: bilinear in (k, x) and non-convex; only locally well-posed under sparse-gradient prior. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `non_blind_deblurring` · **Forward operator:** `shift_invariant_conv` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 512 | | K | — | 15 | | W | px | 512 | | Saturation | — | 0 | | Kernel type | — | motion | | Noise level | — | 0.01 | | Sub pixel shift | — | 0 | | Kernel size error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 128 – 2048 | | K | — | 5 – 51 | | W | px | 128 – 2048 | | Saturation | — | 0.0 – 0.1 | | Noise level | — | 0.001 – 0.1 | | Sub pixel shift | — | 0.0 – 2.0 | | Kernel size error | — | 0.0 – 0.3 | | Kernel shape error | — | 0.0 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 28.0 dB PSNR | Metric | Range | |---|---| | Psnr db | 18.0 – 42.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `1000` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xa9b18a55198557a8cff03b1344962d8a75967d99b1ea3b14a22f0f61c8b090c5` - **Chain tx hash:** `0x2cd1648c4dca93625e463bb7682a8ce8e5c351a2c28a970b6505f755e024a7e3` - **Chain block:** `41555196` --- ## File Mapping This bundle consists of: `L1-382.md`, `L1-382.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-382.md` | Source of truth — edit this | Human or LLM | | `L1-382.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 `L1-382`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-382-001 Image Deblurring Blind-Kernel Spec (GoPro / REDS benchmark family)

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📋 JSON metadata

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  "domain": "Signal Processing",
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    "secondary": "SSIM"
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  "physics_fingerprint": {
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    "difficulty_delta": 3,
    "domain": "Signal Processing",
    "integration_axis": "spatial",
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    "sub_domain": "2D convolutional deblurring",
    "title": "Image Deblurring (non-blind and blind deconvolution)"
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      "K": [
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      "W": [
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      ],
      "kernel_shape_error": [
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      "kernel_size_error": [
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      "noise_level": [
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  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "2D convolutional deblurring",
  "title": "Image Deblurring (non-blind and blind deconvolution)"
}

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