# ⚛  L1 Principle — Electronic Portal Imaging (EPID)

**ID:** `L1-053` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Medical Imaging — *MV X-ray treatment-verification imaging*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D attenuation projection
> **📡 Carrier:** x_ray · **🌫 Noise:** shot poisson
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41552302

---

## 🧠 1. Introduction

**Electronic Portal Imaging (EPID)** is a **linear inverse problem** whose unknown lives in **2D attenuation projection** space, within the **MV X-ray treatment-verification imaging** sub-domain of **Medical Imaging**.

Measurements consist of X-ray photons transmitted through (or scattered by) the sample via a **portal imaging mv** sensing mechanism.

The forward operator applies, in order: L · mv xray source operator; L · patient attenuation operator; D · amorphous silicon panel operator; pixel-level spatial averaging on the detector.

Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered 2D attenuation projection is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is well-conditioned (kappa_eff ~= 9); scatter dominates the stability cliff; optical_glare and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point.

## ⚙ 2. Forward Model

Physical chain: **x** → L · mv xray source → L · patient attenuation → D · amorphous silicon panel → Spatial integration → **y** (detector).

```
y = ∫_A dA `D.amorphous_silicon_panel` `L.patient_attenuation` `L.mv_xray_source` x,    measurements ~ Poisson(αy)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.mv_xray_source` | L · mv xray source operator |
| `L.patient_attenuation` | L · patient attenuation operator |
| `D.amorphous_silicon_panel` | D · amorphous silicon panel operator |
| `int.spatial` | Pixel-level spatial averaging on the detector |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Medical Imaging |
| Sub domain | MV X-ray treatment-verification imaging |
| Carrier | x_ray |
| Problem class | linear_inverse |
| Solution space | 2D_attenuation_projection |
| Noise model | shot_poisson |
| Integration axis | spatial |
| Difficulty delta | 3 |
| L dag | 2.8 |

## 📡 4. Measurement Model

Existence of the recovered 2D attenuation projection is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is well-conditioned (kappa_eff ~= 9); scatter dominates the stability cliff; optical_glare and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point.

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

## 📏 5. Operating Range (Ω)

**Center problem class:** `portal_imaging` · **Forward operator:** `portal_imaging_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 1024 |
| W | px | 1024 |
| Mu | — | 5 |
| Scatter | — | 0.2 |
| Pixel mm | mm | 0.4 |
| Mv energy | — | 6 |
| Optical glare | — | 0 |
| Panel saturation | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 512 |
| W | px | 512 |
| Mu | — | 0.1 – 200 |
| Scatter | — | 0.0 – 0.5 |
| Pixel mm | mm | 0.1 – 2.0 |
| Mv energy | — | 4 – 18 |
| Optical glare | — | 0.0 – 0.3 |
| Panel saturation | — | 0.0 – 0.3 |
| Beam energy drift | — | 0.0 – 0.05 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 25.0

| Metric | Range |
|---|---|
| Psnr db | 5.0 – 45.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `180` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x676d810a8ca49f3336d11f5cfa073fd2f42f6924056eb2ec95986082c396455d`
- **Chain tx hash:** `0x9e7fd79dbfb70f9a70cfaa77bc34413b1cd089fcb53a01f687ad94ea4ff1ae0f`
- **Chain block:** `41552302`

---

## File Mapping

This bundle consists of: `L1-053.md`, `L1-053.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-053.md` | Source of truth — edit this | Human or LLM |
| `L1-053.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 `L1-053`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._