L1 ⚛ L1-038 ⊙ Testnet

Cone-Beam CT (CBCT) — dental / interventional

Medical Imaging · Flat-panel cone-beam CT reconstruction

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⬇ L1-038.md

# ⚛ L1 Principle — Cone-Beam CT (CBCT) — dental / interventional **ID:** `L1-038` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Medical Imaging — *Flat-panel cone-beam CT reconstruction* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D attenuation > **📡 Carrier:** x_ray · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41553358 --- ## 🧠 1. Introduction **Cone-Beam CT (CBCT) — dental / interventional** is a **linear inverse problem** whose unknown lives in **3D attenuation** space, within the **Flat-panel cone-beam CT reconstruction** 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; L · cone beam geometry operator; rotates source / detector to acquire different projections; L · FDK backproject 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 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 ~= 20); scatter dominates the stability cliff; truncation 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 → L · cone beam geometry → Angular scan → L · FDK backproject → Angular integration → **y** (detector). ``` y = ∫dΩ `L.FDK_backproject` R(θ) `L.cone_beam_geometry` I₀(E) x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.xray_source` | Polyenergetic x-ray emission spectrum | | `L.cone_beam_geometry` | L · cone beam geometry operator | | `S.scan.angular` | Rotates source / detector to acquire different projections | | `L.FDK_backproject` | L · fdk backproject operator | | `int.angular` | Integration over the solid angle of incidence/emission | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Medical Imaging | | Sub domain | Flat-panel cone-beam CT reconstruction | | Carrier | x_ray | | Problem class | linear_inverse | | Solution space | 3D_attenuation | | Noise model | shot_poisson | | Integration axis | angular | | Difficulty delta | 5 | | L dag | 4 | ## 📡 4. Measurement Model Existence of the recovered 3D attenuation 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 ~= 20); scatter dominates the stability cliff; truncation 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:** `cbct` · **Forward operator:** `cbct_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 512 | | W | px | 512 | | Z | — | 512 | | Kvp | — | 90 | | Mas | — | 20 | | Scatter | — | 0.2 | | Pixel mm | mm | 0.3 | | Truncation | — | 0 | | N projections | — | 400 | | Patient motion | — | 0 | | Geometric misalignment | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 256 | | W | px | 256 | | Z | — | 64 – 2048 | | Kvp | — | 60 – 120 | | Mas | — | 1 – 200 | | Scatter | — | 0.0 – 0.5 | | Pixel mm | mm | 0.1 – 2.0 | | Truncation | — | 0.0 – 0.3 | | N projections | — | 100 – 2000 | | Beam hardening | — | 0.0 – 0.3 | | Patient motion | — | 0.0 – 0.3 | | Geometric misalignment | — | 0.0 – 2.0 | ## 🎯 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 = `400` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x0167c8e97c6664b8519368f278d9d1fff3ace452d1d642090aec60c2f7e14b27` - **Chain tx hash:** `0x6026b2517c3101582d089bad659fd833ef65a08756ca8a85cf59e7e145352218` - **Chain block:** `41553358` --- ## File Mapping This bundle consists of: `L1-038.md`, `L1-038.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-038.md` | Source of truth — edit this | Human or LLM | | `L1-038.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 `L1-038`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-038.md).
Regenerate L1-038.json so every field matches the Markdown.
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L2-038-001 Cone-Beam CT (CBCT) — dental / interventional Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41553358,
  "chain_hash": "0x0167c8e97c6664b8519368f278d9d1fff3ace452d1d642090aec60c2f7e14b27",
  "chain_tx_hash": "0x6026b2517c3101582d089bad659fd833ef65a08756ca8a85cf59e7e145352218",
  "domain": "Medical Imaging",
  "hardness_fn": {
    "delta": 5,
    "kappa": 400,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
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      "license_hash": null,
      "name": "primary",
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    }
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    "regime": "Existence of the recovered 3D attenuation 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 ~= 20); scatter dominates the stability cliff; truncation 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"
  },
  "physics_fingerprint": {
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    "difficulty_delta": 5,
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    "integration_axis": "angular",
    "noise_model": "shot_poisson",
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      "int.angular"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "xray_ct",
    "solution_space": "3D_attenuation",
    "sub_domain": "Flat-panel cone-beam CT reconstruction",
    "title": "Cone-Beam CT (CBCT) \u2014 dental / interventional"
  },
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    ],
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        "N_projections": 400,
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        "Z": 512,
        "geometric_misalignment": 0.0,
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        "scatter": 0.2,
        "truncation": 0.0
      },
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    },
    "omega_bounds": {
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      ],
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      "Z": [
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      ],
      "beam_hardening": [
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        0.3
      ],
      "geometric_misalignment": [
        0.0,
        2.0
      ],
      "kVp": [
        60,
        120
      ],
      "mAs": [
        1,
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      ],
      "patient_motion": [
        0.0,
        0.3
      ],
      "pixel_mm": [
        0.1,
        2.0
      ],
      "scatter": [
        0.0,
        0.5
      ],
      "truncation": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Flat-panel cone-beam CT reconstruction",
  "title": "Cone-Beam CT (CBCT) \u2014 dental / interventional"
}

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