L1 ⚛ L1-063 ⊙ Testnet

Digital Breast Tomosynthesis (DBT)

Medical Imaging · Limited-angle tomography of the breast

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⬇ L1-063.md

# ⚛ L1 Principle — Digital Breast Tomosynthesis (DBT) **ID:** `L1-063` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Medical Imaging — *Limited-angle tomography of the breast* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D attenuation limited angle > **📡 Carrier:** x_ray · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41553372 --- ## 🧠 1. Introduction **Digital Breast Tomosynthesis (DBT)** is a **linear inverse problem** whose unknown lives in **3D attenuation limited angle** space, within the **Limited-angle tomography of the breast** sub-domain of **Medical Imaging**. Measurements consist of X-ray photons transmitted through (or scattered by) the sample via a **xray ct** sensing mechanism. The forward operator applies, in order: polyenergetic X-ray emission spectrum; S · scan · limited angle operator; L · sart reconstruct operator; integration over the solid angle of incidence/emission. Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered 3D attenuation limited angle 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 moderately conditioned (kappa_eff ~= 18); limited_angle_artifacts dominates the stability cliff; scatter and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega. ## ⚙ 2. Forward Model Physical chain: **x** → X-ray source → S · scan · limited angle → L · sart reconstruct → Angular integration → **y** (detector). ``` y = ∫dΩ `L.sart_reconstruct` `S.scan.limited_angle` I₀(E) x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.xray_source` | Polyenergetic x-ray emission spectrum | | `S.scan.limited_angle` | S · scan · limited angle operator | | `L.sart_reconstruct` | L · sart reconstruct operator | | `int.angular` | Integration over the solid angle of incidence/emission | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Medical Imaging | | Sub domain | Limited-angle tomography of the breast | | Carrier | x_ray | | Problem class | linear_inverse | | Solution space | 3D_attenuation_limited_angle | | Noise model | shot_poisson | | Integration axis | angular | | Difficulty delta | 5 | | L dag | 3.8 | ## 📡 4. Measurement Model Existence of the recovered 3D attenuation limited angle 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 moderately conditioned (kappa_eff ~= 18); limited_angle_artifacts dominates the stability cliff; scatter and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `dbt` · **Forward operator:** `dbt_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 3328 | | W | px | 2560 | | Z | — | 60 | | Kvp | — | 28 | | Mas | — | 60 | | Scatter | — | 0.15 | | Pixel um | µm | 85 | | N projections | — | 15 | | Patient motion | — | 0 | | Tilt range deg | deg | 15 | | Compression variation | — | 0 | | Limited angle artifacts | — | 0.3 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 1664 | | W | px | 1280 | | Z | — | 16 – 200 | | Kvp | — | 22 – 34 | | Mas | — | 10 – 400 | | Scatter | — | 0.0 – 0.3 | | Pixel um | µm | 50 – 200 | | N projections | — | 9 – 25 | | Patient motion | — | 0.0 – 0.3 | | Tilt range deg | deg | 7.5 – 30 | | Compression variation | — | 0.0 – 0.2 | | Limited angle artifacts | — | 0.1 – 0.7 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 27.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `360` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x474b716b33bc75c4888fb038fc166b96487641a2f5f5f5ac9c4e33187eb94927` - **Chain tx hash:** `0xa0078995185ac02bd42d72717bde04a4112362140797523c8aa33acca2287903` - **Chain block:** `41553372` --- ## File Mapping This bundle consists of: `L1-063.md`, `L1-063.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-063.md` | Source of truth — edit this | Human or LLM | | `L1-063.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 `L1-063`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-063.md).
Regenerate L1-063.json so every field matches the Markdown.
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L2-063-001 Digital Breast Tomosynthesis (DBT) Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41553372,
  "chain_hash": "0x474b716b33bc75c4888fb038fc166b96487641a2f5f5f5ac9c4e33187eb94927",
  "chain_tx_hash": "0xa0078995185ac02bd42d72717bde04a4112362140797523c8aa33acca2287903",
  "domain": "Medical Imaging",
  "hardness_fn": {
    "delta": 5,
    "kappa": 360,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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    "regime": "Existence of the recovered 3D attenuation limited angle 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 moderately conditioned (kappa_eff ~= 18); limited_angle_artifacts dominates the stability cliff; scatter and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega.",
    "secondary": "SSIM"
  },
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    "L_DAG": 3.8,
    "carrier": "x_ray",
    "difficulty_delta": 5,
    "domain": "Medical Imaging",
    "integration_axis": "angular",
    "noise_model": "shot_poisson",
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      "S.scan.limited_angle",
      "L.sart_reconstruct",
      "int.angular"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "xray_ct",
    "solution_space": "3D_attenuation_limited_angle",
    "sub_domain": "Limited-angle tomography of the breast",
    "title": "Digital Breast Tomosynthesis (DBT)"
  },
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      "scatter",
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    ],
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    "center_spec": {
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      "input_format": "measurement_only",
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        "N_projections": 15,
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        "limited_angle_artifacts": 0.3,
        "mAs": 60,
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        "scatter": 0.15,
        "tilt_range_deg": 15
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    "omega_bounds": {
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      "N_projections": [
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      "Z": [
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      "compression_variation": [
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      "kVp": [
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        34
      ],
      "limited_angle_artifacts": [
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        0.7
      ],
      "mAs": [
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      ],
      "patient_motion": [
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        0.3
      ],
      "pixel_um": [
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      ],
      "scatter": [
        0.0,
        0.3
      ],
      "tilt_range_deg": [
        7.5,
        30
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Limited-angle tomography of the breast",
  "title": "Digital Breast Tomosynthesis (DBT)"
}

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