L1 ⚛ L1-026 ⊙ Testnet

Single-Pixel Imaging (random basis compressive sensing)

Compressive Imaging · Single-pixel / single-detector imaging

⬇ Download bundle 🚀 Submit to mainnet — earn 100 PWM + 5% royalty

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-026.md

# ⚛ L1 Principle — Single-Pixel Imaging (random basis compressive sensing) **ID:** `L1-026` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Compressive Imaging — *Single-pixel / single-detector imaging* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D spatial > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41547811 --- ## 🧠 1. Introduction **Single-Pixel Imaging (random basis compressive sensing)** is a **linear inverse problem** whose unknown lives in **2D spatial** space, within the **Single-pixel / single-detector imaging** sub-domain of **Compressive Imaging**. Measurements consist of photons collected by an optical detector via a **structured illumination** sensing mechanism. The forward operator applies, in order: S · pattern · random operator; L · inner product operator; pixel-level spatial averaging on the detector; D · scalar operator. Observations are corrupted by additive Gaussian noise. Underdetermined (m << n) compressive recovery; random sensing matrices with i.i.d. Bernoulli/Gaussian entries satisfy RIP w.h.p. when m >= C * s * log(n/s) for s-sparse signals in a known basis. ## ⚙ 2. Forward Model Physical chain: **x** → S · pattern · random → L · inner product → Spatial integration → D · scalar → **y** (detector). ``` y = `D.scalar` ∫_A dA `L.inner_product` `S.pattern.random` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `S.pattern.random` | S · pattern · random operator | | `L.inner_product` | L · inner product operator | | `int.spatial` | Pixel-level spatial averaging on the detector | | `D.scalar` | D · scalar operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Compressive Imaging | | Sub domain | Single-pixel / single-detector imaging | | Carrier | photon | | Problem class | linear_inverse | | Solution space | 2D_spatial | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Underdetermined (m << n) compressive recovery; random sensing matrices with i.i.d. Bernoulli/Gaussian entries satisfy RIP w.h.p. when m >= C * s * log(n/s) for s-sparse signals in a known basis. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `compressed_sensing_recovery` · **Forward operator:** `random_projection` **Center point:** | Parameter | Unit | Value | |---|---|---| | N pixels | — | 4096 | | Gain alpha | — | 0 | | Illum sigma | — | 0 | | Noise level | — | 0.01 | | Sampling ratio | — | 0.25 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N pixels | — | 1024 – 65536 | | Gain alpha | — | 0.0 – 0.003 | | Dark offset | — | 0.0 – 0.02 | | Illum sigma | — | 0.0 – 15.0 | | Noise level | — | 0.001 – 0.05 | | Sampling ratio | — | 0.05 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 27.0 dB PSNR | Metric | Range | |---|---| | Psnr db | 18.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `4000` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x9530ddad080c15de3e2194d2487f390339dd06a6f57560f5c6196e85c3c655cb` - **Chain tx hash:** `0xdb29b0671dfe88bafb7b42624f90e28dd67bf064cd72ced85046d7feea520814` - **Chain block:** `41547811` --- ## File Mapping This bundle consists of: `L1-026.md`, `L1-026.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-026.md` | Source of truth — edit this | Human or LLM | | `L1-026.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 `L1-026`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

📝 Polish this artifact in your LLM

Download the files on the right.
Paste the Markdown into ChatGPT / Claude / Gemini and edit freely.
Send your edited Markdown back with the prompt below.
Save the regenerated JSON, then submit via /submit.

Prompt to give your LLM

Read the attached Markdown (L1-026.md).
Regenerate L1-026.json so every field matches the Markdown.
Preserve the schema documented in the File Mapping footer at the bottom of the MD.
Output each file in its own fenced code block tagged with the filename.

⌥ Hierarchy

Upstream lineage and downstream children

↓ L2 Spec 1 child ▾

L2-026-001 Single-Pixel Imaging Mismatch-Only Spec

⬇ Download bundle

2 files · click to download

📋 JSON metadata

{
  "artifact_id": "L1-026",
  "chain_block": 41547811,
  "chain_hash": "0x9530ddad080c15de3e2194d2487f390339dd06a6f57560f5c6196e85c3c655cb",
  "chain_tx_hash": "0xdb29b0671dfe88bafb7b42624f90e28dd67bf064cd72ced85046d7feea520814",
  "domain": "Compressive Imaging",
  "hardness_fn": {
    "delta": 3,
    "kappa": 4000,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Underdetermined (m \u003c\u003c n) compressive recovery; random sensing matrices with i.i.d. Bernoulli/Gaussian entries satisfy RIP w.h.p. when m \u003e= C * s * log(n/s) for s-sparse signals in a known basis.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "photon",
    "difficulty_delta": 3,
    "domain": "Compressive Imaging",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "S.pattern.random",
      "L.inner_product",
      "int.spatial",
      "D.scalar"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "structured_illumination",
    "solution_space": "2D_spatial",
    "sub_domain": "Single-pixel / single-detector imaging",
    "title": "Single-Pixel Imaging (random basis compressive sensing)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "random_projection",
      "hadamard",
      "noiselet",
      "gaussian_sensing"
    ],
    "allowed_omega_dimensions": [
      "n_pixels",
      "sampling_ratio",
      "noise_level",
      "gain_alpha",
      "illum_sigma",
      "dark_offset"
    ],
    "allowed_problem_classes": [
      "compressed_sensing_recovery",
      "sparse_recovery",
      "basis_pursuit"
    ],
    "center_spec": {
      "epsilon_fn_center": "27.0 dB PSNR",
      "forward_operator": "random_projection",
      "input_format": "measurement_plus_pattern_matrix",
      "omega": {
        "gain_alpha": 0.0,
        "illum_sigma": 0.0,
        "n_pixels": 4096,
        "noise_level": 0.01,
        "sampling_ratio": 0.25
      },
      "problem_class": "compressed_sensing_recovery"
    },
    "epsilon_bounds": {
      "psnr_db": [
        18.0,
        40.0
      ]
    },
    "omega_bounds": {
      "dark_offset": [
        0.0,
        0.02
      ],
      "gain_alpha": [
        0.0,
        0.003
      ],
      "illum_sigma": [
        0.0,
        15.0
      ],
      "n_pixels": [
        1024,
        65536
      ],
      "noise_level": [
        0.001,
        0.05
      ],
      "sampling_ratio": [
        0.05,
        0.5
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Single-pixel / single-detector imaging",
  "title": "Single-Pixel Imaging (random basis compressive sensing)"
}

🎁

Earn PWM by promoting this to mainnet

• 100 PWM one-time grant on mainnet promotion
• 5% upstream royalty on every downstream L4 mining event, forever
• Your wallet is enrolled the moment the founder accepts

🚀 Submit to mainnet →

How: Download the bundle above → polish the Markdown in ChatGPT / Claude / Gemini → submit your version → founder reviews → mainnet.