# ⚛  L1 Principle — Coded-Exposure Imaging for Motion Deblur

**ID:** `L1-077` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Computational Photography — *Temporal coding for motion robust imaging*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D spatial
> **📡 Carrier:** photon · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554170

---

## 🧠 1. Introduction

**Coded-Exposure Imaging for Motion Deblur** is a **linear inverse problem** whose unknown lives in **2D spatial** space, within the **Temporal coding for motion robust imaging** sub-domain of **Computational Photography**.

Measurements consist of photons collected by an optical detector via a **coded temporal shutter** sensing mechanism.

The forward operator applies, in order: S · temporal · coded operator; L · conv · motion operator; detector accumulates flux over the exposure window.

Observations are corrupted by additive Gaussian noise. Coded kernel h_c is chosen to have approximately flat magnitude response (MURA or optimal binary codes); OTF is nonzero across full passband, so Wiener deconvolution is well-conditioned. Stability dominated by motion-direction / velocity mismatch and saturation clipping.

## ⚙ 2. Forward Model

Physical chain: **x** → S · temporal · coded → L · conv · motion → Temporal integration → **y** (detector).

```
y = ∫_t dt `L.conv.motion` `S.temporal.coded` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `S.temporal.coded` | S · temporal · coded operator |
| `L.conv.motion` | L · conv · motion operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Computational Photography |
| Sub domain | Temporal coding for motion robust imaging |
| Carrier | photon |
| Problem class | linear_inverse |
| Solution space | 2D_spatial |
| Noise model | gaussian |
| Integration axis | temporal |
| Difficulty delta | 3 |
| L dag | 2.5 |

## 📡 4. Measurement Model

Coded kernel h_c is chosen to have approximately flat magnitude response (MURA or optimal binary codes); OTF is nonzero across full passband, so Wiener deconvolution is well-conditioned. Stability dominated by motion-direction / velocity mismatch and saturation clipping.

| Metric | Value |
|---|---|
| Metric | PSNR_dB |
| Secondary | SSIM |

## 📏 5. Operating Range (Ω)

**Center problem class:** `motion_deblur_coded_exposure` · **Forward operator:** `coded_exposure_convolution`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 1024 |
| W | px | 1024 |
| T ms | ms | 52 |
| Velocity px | — | 20 |
| Photon count | — | 1000 |
| Code length bits | — | 52 |
| Motion velocity error | — | 0 |
| Motion direction error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 256 – 4096 |
| W | px | 256 – 4096 |
| T ms | ms | 5 – 200 |
| Velocity px | — | 1.0 – 100.0 |
| Photon count | — | 50 – 10000 |
| Saturation clip | — | 0.0 – 0.1 |
| Code length bits | — | 16 – 128 |
| Motion velocity error | — | 0.0 – 0.5 |
| Motion direction error | — | 0.0 – 0.3 |
| Exposure duration error | — | 0.0 – 0.2 |

## 🎯 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 = `900` and δ = `3`.

## 💾 8. Reference Dataset

- **primary** · weight 1.0 · IPFS _(not pinned yet)_

## 9. On-chain Registration

- **Chain hash:** `0xb6f8a13d8edc6c4a4df0bc75d347c52640a7a706eeee51de7bd9ef6840d3d440`
- **Chain tx hash:** `0x672983fc701f89da4e626c4fdd69915f90d2fee45d9fc54c8edfb7de2b85914a`
- **Chain block:** `41554170`

---

## File Mapping

This bundle consists of: `L1-077.md`, `L1-077.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-077.md` | Source of truth — edit this | Human or LLM |
| `L1-077.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 `L1-077`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._