# ⚛  L1 Principle — Coded Aperture Snapshot Spectral Imaging (CASSI)

**ID:** `L1-003` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Compressive Imaging — *Hyperspectral snapshot*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D spectral
> **📡 Carrier:** photon · **🌫 Noise:** shot poisson
> **⚖ Difficulty (δ):** — · **⛓ Block:** 41421557

---

## 🧠 1. Introduction

**Coded Aperture Snapshot Spectral Imaging (CASSI)** is a **linear inverse problem** whose unknown lives in **3D spectral** space, within the **Hyperspectral snapshot** sub-domain of **Compressive Imaging**.

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

The forward operator applies, in order: replicates a 2-D mask across spectral bands; element-wise multiplication by a binary mask; wavelength-dependent pixel shift along the dispersion axis; detector sums all spectral bands.

Observations are corrupted by Poisson shot noise from quantum-limited detection. underdetermined compressive recovery (N_bands:1 compression); binary random mask at 50% fill satisfies RIP-like conditions; recovery unique under spectral sparsity prior; stability governed by mask quality and calibration accuracy.

## ⚙ 2. Forward Model

Physical chain: **x** → Spectral broadcast → Binary coded aperture → Spectral dispersion (shear) → Spectral integration → **y** (detector).

```
y(x,y) = sum_lambda C(x, y + a*lambda) * f(x, y + a*lambda, lambda) + n(x,y)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.broadcast.spectral` | Replicates a 2-d mask across spectral bands |
| `L.diag.binary` | Element-wise multiplication by a binary mask |
| `L.shear.spectral` | Wavelength-dependent pixel shift along the dispersion axis |
| `int.spectral` | Detector sums all spectral bands |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Compressive Imaging |
| Sub domain | Hyperspectral snapshot |
| Carrier | photon |
| Problem class | linear_inverse |
| Solution space | 3D_spectral |
| Noise model | shot_poisson |
| Integration axis | spectral |
| L dag | 3.7 |

## 📡 4. Measurement Model

underdetermined compressive recovery (N_bands:1 compression); binary random mask at 50% fill satisfies RIP-like conditions; recovery unique under spectral sparsity prior; stability governed by mask quality and calibration accuracy.

| Metric | Value |
|---|---|
| Metric | PSNR_dB |

## ⚖ 6. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `5000`.

## 💾 7. Reference Dataset

- **KAIST-30** · weight 0.5 · IPFS _(not pinned yet)_
- **CAVE multispectral** · weight 0.3 · IPFS _(not pinned yet)_
- **ICVL hyperspectral** · weight 0.2 · IPFS _(not pinned yet)_

## 8. On-chain Registration

- **Chain hash:** `0xe3b1328c66835cd729fa50650ef1d1bac4aa407807d6d97d4979e988a99a51ea`
- **Chain tx hash:** `0xcdf5bc704e679e719990043b412482ce1ab4df0a4176e6d7881a234b855546f9`
- **Chain block:** `41421557`

**Staked PWM:** 5000.0

---

## File Mapping

This bundle consists of: `L1-003.md`, `L1-003.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-003.md` | Source of truth — edit this | Human or LLM |
| `L1-003.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 `L1-003`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._