L1 ⚛ L1-040 ⊙ Testnet

Diffuse Optical Tomography (DOT)

Medical Imaging · Near-IR scattering-based functional imaging

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⬇ L1-040.md

# ⚛ L1 Principle — Diffuse Optical Tomography (DOT) **ID:** `L1-040` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Medical Imaging — *Near-IR scattering-based functional imaging* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 3D optical absorption > **📡 Carrier:** photon · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41553385 --- ## 🧠 1. Introduction **Diffuse Optical Tomography (DOT)** is a **nonlinear inverse problem** whose unknown lives in **3D optical absorption** space, within the **Near-IR scattering-based functional imaging** sub-domain of **Medical Imaging**. Measurements consist of photons collected by an optical detector via a **near infrared diffusion** sensing mechanism. The forward operator applies, in order: L · nir source operator; L · diffusion propagation operator; S · scan · source detector operator; pixel-level spatial averaging on the detector. Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered 3D optical absorption is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 30); tissue_scattering dominates the stability cliff; anatomical_prior_error 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** → L · nir source → L · diffusion propagation → S · scan · source detector → Spatial integration → **y** (detector). ``` y = ∫_A dA `S.scan.source_detector` `L.diffusion_propagation` `L.nir_source` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.nir_source` | L · nir source operator | | `L.diffusion_propagation` | L · diffusion propagation operator | | `S.scan.source_detector` | S · scan · source detector operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Medical Imaging | | Sub domain | Near-IR scattering-based functional imaging | | Carrier | photon | | Problem class | nonlinear_inverse | | Solution space | 3D_optical_absorption | | Noise model | shot_poisson | | Integration axis | spatial | | Difficulty delta | 10 | | L dag | 4 | ## 📡 4. Measurement Model Existence of the recovered 3D optical absorption is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 30); tissue_scattering dominates the stability cliff; anatomical_prior_error 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:** `dot` · **Forward operator:** `dot_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 25 | | Motion | — | 0 | | N sources | — | 32 | | Lambda nm | nm | 760 | | N detectors | — | 32 | | Partial volume | — | 0.1 | | Tissue scattering | — | 10 | | Source distance cm | — | 3.5 | | Anatomical prior error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | 0.0 – 35.0 | | Motion | — | 0.0 – 0.3 | | N sources | — | 8 – 256 | | Lambda nm | nm | 650 – 900 | | N detectors | — | 8 – 256 | | Partial volume | — | 0.0 – 0.5 | | Tissue scattering | — | 5.0 – 20.0 | | Source distance cm | — | 1.0 – 10.0 | | Anatomical prior error | — | 0.0 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 18.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `600` and δ = `10`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xb4872c1d2d2dcb7a5ef7e22a621bb2298ea0ab7a90ad8acec35cf81509135a4b` - **Chain tx hash:** `0x45e960be5d35ae5d2adaeb980d395acdb6a2a60427236e96d9b4892a99ccf402` - **Chain block:** `41553385` --- ## File Mapping This bundle consists of: `L1-040.md`, `L1-040.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-040.md` | Source of truth — edit this | Human or LLM | | `L1-040.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 `L1-040`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-040.md).
Regenerate L1-040.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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L2-040-001 Diffuse Optical Tomography (DOT) Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-040",
  "chain_block": 41553385,
  "chain_hash": "0xb4872c1d2d2dcb7a5ef7e22a621bb2298ea0ab7a90ad8acec35cf81509135a4b",
  "chain_tx_hash": "0x45e960be5d35ae5d2adaeb980d395acdb6a2a60427236e96d9b4892a99ccf402",
  "domain": "Medical Imaging",
  "hardness_fn": {
    "delta": 10,
    "kappa": 600,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
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  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Existence of the recovered 3D optical absorption is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 30); tissue_scattering dominates the stability cliff; anatomical_prior_error 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": {
    "L_DAG": 4.0,
    "carrier": "photon",
    "difficulty_delta": 10,
    "domain": "Medical Imaging",
    "integration_axis": "spatial",
    "noise_model": "shot_poisson",
    "primitives": [
      "L.nir_source",
      "L.diffusion_propagation",
      "S.scan.source_detector",
      "int.spatial"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "near_infrared_diffusion",
    "solution_space": "3D_optical_absorption",
    "sub_domain": "Near-IR scattering-based functional imaging",
    "title": "Diffuse Optical Tomography (DOT)"
  },
  "size_tiers": {
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      "dot_forward"
    ],
    "allowed_omega_dimensions": [
      "N_sources",
      "N_detectors",
      "lambda_nm",
      "source_distance_cm",
      "SNR_dB",
      "tissue_scattering",
      "anatomical_prior_error",
      "partial_volume",
      "motion",
      "tissue_scattering",
      "anatomical_prior_error",
      "partial_volume",
      "motion"
    ],
    "allowed_problem_classes": [
      "dot"
    ],
    "center_spec": {
      "epsilon_fn_center": "18.0",
      "forward_operator": "dot_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_detectors": 32,
        "N_sources": 32,
        "SNR_dB": 25,
        "anatomical_prior_error": 0.0,
        "lambda_nm": 760,
        "motion": 0.0,
        "partial_volume": 0.1,
        "source_distance_cm": 3.5,
        "tissue_scattering": 10.0
      },
      "problem_class": "dot"
    },
    "epsilon_bounds": {
      "psnr_db": [
        5.0,
        45.0
      ]
    },
    "omega_bounds": {
      "N_detectors": [
        8,
        256
      ],
      "N_sources": [
        8,
        256
      ],
      "SNR_dB": [
        0.0,
        35.0
      ],
      "anatomical_prior_error": [
        0.0,
        0.5
      ],
      "lambda_nm": [
        650,
        900
      ],
      "motion": [
        0.0,
        0.3
      ],
      "partial_volume": [
        0.0,
        0.5
      ],
      "source_distance_cm": [
        1.0,
        10.0
      ],
      "tissue_scattering": [
        5.0,
        20.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Near-IR scattering-based functional imaging",
  "title": "Diffuse Optical Tomography (DOT)"
}

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