L1 ⚛ L1-041 ⊙ Testnet

Photoacoustic Tomography (PAT)

Medical Imaging · Hybrid optical-acoustic absorption imaging

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⬇ L1-041.md

# ⚛ L1 Principle — Photoacoustic Tomography (PAT) **ID:** `L1-041` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Medical Imaging — *Hybrid optical-acoustic absorption imaging* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 3D optical absorption > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41552301 --- ## 🧠 1. Introduction **Photoacoustic Tomography (PAT)** is a **nonlinear inverse problem** whose unknown lives in **3D optical absorption** space, within the **Hybrid optical-acoustic absorption imaging** sub-domain of **Medical Imaging**. Measurements consist of photons collected by an optical detector via a **photoacoustic pa** sensing mechanism. The forward operator applies, in order: L · laser pulse excite operator; L · thermoacoustic generation operator; D · ultrasound array operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. 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 ~= 22); sound_speed_heterogeneity dominates the stability cliff; limited_view_geometry and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise 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 · laser pulse excite → L · thermoacoustic generation → D · ultrasound array → Temporal integration → **y** (detector). ``` y = ∫_t dt `D.ultrasound_array` `L.thermoacoustic_generation` `L.laser_pulse_excite` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.laser_pulse_excite` | L · laser pulse excite operator | | `L.thermoacoustic_generation` | L · thermoacoustic generation operator | | `D.ultrasound_array` | D · ultrasound array operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Medical Imaging | | Sub domain | Hybrid optical-acoustic absorption imaging | | Carrier | photon | | Problem class | nonlinear_inverse | | Solution space | 3D_optical_absorption | | Noise model | gaussian | | Integration axis | angular | | Difficulty delta | 5 | | L dag | 4.2 | ## 📡 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 ~= 22); sound_speed_heterogeneity dominates the stability cliff; limited_view_geometry and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise 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:** `pat` · **Forward operator:** `pat_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | Z | — | 128 | | Snr db | dB | 22 | | Lambda nm | nm | 800 | | N transducers | — | 256 | | Limited view geometry | — | 0 | | Laser fluence variation | — | 0 | | Sound speed heterogeneity | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 64 | | W | px | 64 | | Z | — | 16 – 512 | | Snr db | dB | 0.0 – 35.0 | | Lambda nm | nm | 650 – 1064 | | N transducers | — | 32 – 1024 | | Coupling medium | — | 0.0 – 0.3 | | Limited view geometry | — | 0.0 – 0.6 | | Laser fluence variation | — | 0.0 – 0.3 | | Sound speed heterogeneity | — | 0.0 – 0.05 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 23.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `440` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x4e4dd0f446a8051c55565628c90a06acce663bfc12069182bf5d709d141507d7` - **Chain tx hash:** `0x32308413b53b9f8e857ad9384922297b392b984674da7f7865007cb9c255637e` - **Chain block:** `41552301` --- ## File Mapping This bundle consists of: `L1-041.md`, `L1-041.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-041.md` | Source of truth — edit this | Human or LLM | | `L1-041.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 `L1-041`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-041.md).
Regenerate L1-041.json so every field matches the Markdown.
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L2-041-001 Photoacoustic Tomography (PAT) Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41552301,
  "chain_hash": "0x4e4dd0f446a8051c55565628c90a06acce663bfc12069182bf5d709d141507d7",
  "chain_tx_hash": "0x32308413b53b9f8e857ad9384922297b392b984674da7f7865007cb9c255637e",
  "domain": "Medical Imaging",
  "hardness_fn": {
    "delta": 5,
    "kappa": 440,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
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      "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 ~= 22); sound_speed_heterogeneity dominates the stability cliff; limited_view_geometry and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise 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": 4.2,
    "carrier": "photon",
    "difficulty_delta": 5,
    "domain": "Medical Imaging",
    "integration_axis": "angular",
    "noise_model": "gaussian",
    "primitives": [
      "L.laser_pulse_excite",
      "L.thermoacoustic_generation",
      "D.ultrasound_array",
      "int.temporal"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "photoacoustic_pa",
    "solution_space": "3D_optical_absorption",
    "sub_domain": "Hybrid optical-acoustic absorption imaging",
    "title": "Photoacoustic Tomography (PAT)"
  },
  "size_tiers": {
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      "Z",
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      "SNR_dB",
      "sound_speed_heterogeneity",
      "limited_view_geometry",
      "laser_fluence_variation",
      "sound_speed_heterogeneity",
      "limited_view_geometry",
      "laser_fluence_variation",
      "coupling_medium"
    ],
    "allowed_problem_classes": [
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    ],
    "center_spec": {
      "epsilon_fn_center": "23.0",
      "forward_operator": "pat_forward",
      "input_format": "measurement_only",
      "omega": {
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        "N_transducers": 256,
        "SNR_dB": 22,
        "W": 256,
        "Z": 128,
        "lambda_nm": 800,
        "laser_fluence_variation": 0.0,
        "limited_view_geometry": 0.0,
        "sound_speed_heterogeneity": 0.0
      },
      "problem_class": "pat"
    },
    "epsilon_bounds": {
      "psnr_db": [
        5.0,
        45.0
      ]
    },
    "omega_bounds": {
      "H": 64,
      "N_transducers": [
        32,
        1024
      ],
      "SNR_dB": [
        0.0,
        35.0
      ],
      "W": 64,
      "Z": [
        16,
        512
      ],
      "coupling_medium": [
        0.0,
        0.3
      ],
      "lambda_nm": [
        650,
        1064
      ],
      "laser_fluence_variation": [
        0.0,
        0.3
      ],
      "limited_view_geometry": [
        0.0,
        0.6
      ],
      "sound_speed_heterogeneity": [
        0.0,
        0.05
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Hybrid optical-acoustic absorption imaging",
  "title": "Photoacoustic Tomography (PAT)"
}

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