L1 ⚛ L1-025 ⊙ Testnet

Coded Aperture Snapshot Spectral Imaging (CASSI)

Compressive Imaging · Hyperspectral snapshot

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⬇ L1-025.md

# ⚛ 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._

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Read the attached Markdown (L1-025.md).
Regenerate L1-025.json so every field matches the Markdown.
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Output each file in its own fenced code block tagged with the filename.

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L2-025-001 CASSI Mismatch-Only Spec (KAIST benchmark family)

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📋 JSON metadata

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  "chain_block": 41554169,
  "chain_hash": "0x03b714a728cf9f81ea6445e73adcd02ed18420babc2a335421ed8d0f594cf19f",
  "chain_tx_hash": "0x8238f44f380512995080df4fe095f6c190530b7e5ac5feec9e9a21afeccb56bb",
  "domain": "Compressive Imaging",
  "hardness_fn": {
    "delta": 3,
    "kappa": 5000,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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      "name": "primary",
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  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "underdetermined compressive recovery (N_bands:1 compression); binary random mask at 50% fill satisfies RIP-like conditions; recovery unique under spectral sparsity prior.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.7,
    "carrier": "photon",
    "difficulty_delta": 3,
    "domain": "Compressive Imaging",
    "integration_axis": "spectral",
    "noise_model": "shot_poisson",
    "primitives": [
      "L.broadcast.spectral",
      "L.diag.binary",
      "L.shear.spectral",
      "int.spectral"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "coded_aperture",
    "solution_space": "3D_spectral",
    "sub_domain": "Hyperspectral snapshot",
    "title": "Coded Aperture Snapshot Spectral Imaging (CASSI)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "coded_aperture_spectral"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "N_bands",
      "mask_density",
      "noise_level",
      "disp_a1_error",
      "disp_alpha_error",
      "mask_dx",
      "mask_dy",
      "mask_theta"
    ],
    "allowed_problem_classes": [
      "spectral_reconstruction",
      "hyperspectral_unmixing"
    ],
    "center_spec": {
      "epsilon_fn_center": "28.0 dB PSNR",
      "forward_operator": "coded_aperture_spectral",
      "input_format": "measurement_only",
      "omega": {
        "H": 256,
        "N_bands": 28,
        "W": 256,
        "disp_a1_error": 0.0,
        "disp_alpha_error": 0.0,
        "mask_density": 0.5,
        "mask_dx": 0.0,
        "mask_dy": 0.0,
        "mask_theta": 0.0,
        "noise_level": 0.01
      },
      "problem_class": "spectral_reconstruction"
    },
    "epsilon_bounds": {
      "psnr_db": [
        20.0,
        45.0
      ]
    },
    "omega_bounds": {
      "H": [
        64,
        2048
      ],
      "N_bands": [
        8,
        128
      ],
      "W": [
        64,
        2048
      ],
      "disp_a1_error": [
        0.0,
        0.05
      ],
      "disp_alpha_error": [
        0.0,
        0.3
      ],
      "mask_density": [
        0.3,
        0.7
      ],
      "mask_dx": [
        0.0,
        1.0
      ],
      "mask_dy": [
        0.0,
        1.0
      ],
      "mask_theta": [
        0.0,
        0.15
      ],
      "noise_level": [
        0.001,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Hyperspectral snapshot",
  "title": "Coded Aperture Snapshot Spectral Imaging (CASSI)"
}

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