# ⚛  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._