# ⚛  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._