L1 ⚛ L1-066 ⊙ Testnet

Electrical Impedance Tomography (EIT)

Medical Imaging · Electrical-conductivity internal imaging via surface electrodes

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⬇ L1-066.md

# ⚛ L1 Principle — Electrical Impedance Tomography (EIT) **ID:** `L1-066` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Medical Imaging — *Electrical-conductivity internal imaging via surface electrodes* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 2D conductivity map > **📡 Carrier:** radio_wave · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41553359 --- ## 🧠 1. Introduction **Electrical Impedance Tomography (EIT)** is a **nonlinear inverse problem** whose unknown lives in **2D conductivity map** space, within the **Electrical-conductivity internal imaging via surface electrodes** sub-domain of **Medical Imaging**. Measurements consist of radio-frequency electromagnetic waves via a **electrical impedance** sensing mechanism. The forward operator applies, in order: L · current injection operator; D · voltage measure operator; L · inverse poisson operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Existence of the recovered 2D conductivity map 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); electrode_contact dominates the stability cliff; model_geometry_error 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 · current injection → D · voltage measure → L · inverse poisson → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.inverse_poisson` `D.voltage_measure` `L.current_injection` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.current_injection` | L · current injection operator | | `D.voltage_measure` | D · voltage measure operator | | `L.inverse_poisson` | L · inverse poisson operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Medical Imaging | | Sub domain | Electrical-conductivity internal imaging via surface electrodes | | Carrier | radio_wave | | Problem class | nonlinear_inverse | | Solution space | 2D_conductivity_map | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 10 | | L dag | 4.5 | ## 📡 4. Measurement Model Existence of the recovered 2D conductivity map 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); electrode_contact dominates the stability cliff; model_geometry_error 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:** `eit` · **Forward operator:** `eit_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 128 | | W | px | 128 | | Drift | — | 0 | | Snr db | dB | 25 | | N patterns | — | 16 | | N electrodes | — | 32 | | Electrode contact | — | 1 | | Noise amplification | — | 0.1 | | Model geometry error | — | 0.05 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 – 512 | | W | px | 32 – 512 | | Drift | — | 0.0 – 0.3 | | Snr db | dB | 0.0 – 40.0 | | N patterns | — | 4 – 128 | | N electrodes | — | 8 – 256 | | Electrode contact | — | 0.3 – 1.0 | | Noise amplification | — | 0.0 – 0.5 | | Model geometry error | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 14.0 | 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:** `0xeb0170bb6d873e52de6292d1472e2e155e54a013bf626ef4cf4859f9f29211ae` - **Chain tx hash:** `0x150005ce17882e20bd51b492c655298630313d56c326de5b76fe3f71f14717d5` - **Chain block:** `41553359` --- ## File Mapping This bundle consists of: `L1-066.md`, `L1-066.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-066.md` | Source of truth — edit this | Human or LLM | | `L1-066.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 `L1-066`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-066.md).
Regenerate L1-066.json so every field matches the Markdown.
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L2-066-001 Electrical Impedance Tomography (EIT) Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-066",
  "chain_block": 41553359,
  "chain_hash": "0xeb0170bb6d873e52de6292d1472e2e155e54a013bf626ef4cf4859f9f29211ae",
  "chain_tx_hash": "0x150005ce17882e20bd51b492c655298630313d56c326de5b76fe3f71f14717d5",
  "domain": "Medical Imaging",
  "hardness_fn": {
    "delta": 10,
    "kappa": 600,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
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      "license_hash": null,
      "name": "primary",
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    }
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  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Existence of the recovered 2D conductivity map 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); electrode_contact dominates the stability cliff; model_geometry_error 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": 4.5,
    "carrier": "radio_wave",
    "difficulty_delta": 10,
    "domain": "Medical Imaging",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.current_injection",
      "D.voltage_measure",
      "L.inverse_poisson",
      "int.spatial"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "electrical_impedance",
    "solution_space": "2D_conductivity_map",
    "sub_domain": "Electrical-conductivity internal imaging via surface electrodes",
    "title": "Electrical Impedance Tomography (EIT)"
  },
  "size_tiers": {
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      "W",
      "SNR_dB",
      "electrode_contact",
      "model_geometry_error",
      "noise_amplification",
      "drift",
      "electrode_contact",
      "model_geometry_error",
      "noise_amplification",
      "drift"
    ],
    "allowed_problem_classes": [
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    ],
    "center_spec": {
      "epsilon_fn_center": "14.0",
      "forward_operator": "eit_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 128,
        "N_electrodes": 32,
        "N_patterns": 16,
        "SNR_dB": 25,
        "W": 128,
        "drift": 0.0,
        "electrode_contact": 1.0,
        "model_geometry_error": 0.05,
        "noise_amplification": 0.1
      },
      "problem_class": "eit"
    },
    "epsilon_bounds": {
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        45.0
      ]
    },
    "omega_bounds": {
      "H": [
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        512
      ],
      "N_electrodes": [
        8,
        256
      ],
      "N_patterns": [
        4,
        128
      ],
      "SNR_dB": [
        0.0,
        40.0
      ],
      "W": [
        32,
        512
      ],
      "drift": [
        0.0,
        0.3
      ],
      "electrode_contact": [
        0.3,
        1.0
      ],
      "model_geometry_error": [
        0.0,
        0.3
      ],
      "noise_amplification": [
        0.0,
        0.5
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Electrical-conductivity internal imaging via surface electrodes",
  "title": "Electrical Impedance Tomography (EIT)"
}

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