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

**ID:** `L1-025` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Compressive Imaging — *Hyperspectral snapshot*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D spectral
> **📡 Carrier:** photon · **🌫 Noise:** shot poisson
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554169

---

## 🧠 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.

## ⚙ 2. Forward Model

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

```
y = Σ_λ S_λ M ⊙ B_λ x,    measurements ~ Poisson(αy)
```

**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 |
| Difficulty delta | 3 |
| 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.

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

## 📏 5. Operating Range (Ω)

**Center problem class:** `spectral_reconstruction` · **Forward operator:** `coded_aperture_spectral`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 256 |
| W | px | 256 |
| N bands | bands | 28 |
| Mask dx | — | 0 |
| Mask dy | — | 0 |
| Mask theta | — | 0 |
| Noise level | — | 0.01 |
| Mask density | — | 0.5 |
| Disp a1 error | — | 0 |
| Disp alpha error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 64 – 2048 |
| W | px | 64 – 2048 |
| N bands | bands | 8 – 128 |
| Mask dx | — | 0.0 – 1.0 |
| Mask dy | — | 0.0 – 1.0 |
| Mask theta | — | 0.0 – 0.15 |
| Noise level | — | 0.001 – 0.1 |
| Mask density | — | 0.3 – 0.7 |
| Disp a1 error | — | 0.0 – 0.05 |
| Disp alpha error | — | 0.0 – 0.3 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 28.0 dB PSNR

| Metric | Range |
|---|---|
| Psnr db | 20.0 – 45.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `5000` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x03b714a728cf9f81ea6445e73adcd02ed18420babc2a335421ed8d0f594cf19f`
- **Chain tx hash:** `0x8238f44f380512995080df4fe095f6c190530b7e5ac5feec9e9a21afeccb56bb`
- **Chain block:** `41554169`

---

## File Mapping

This bundle consists of: `L1-025.md`, `L1-025.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-025.md` | Source of truth — edit this | Human or LLM |
| `L1-025.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 `L1-025`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._