L1 ⚛ L1-109 ⊙ Testnet

Polarimetric SAR (PolSAR) — full-polarimetric decomposition

Remote Sensing · Polarimetric scattering analysis

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⬇ L1-109.md

# ⚛ L1 Principle — Polarimetric SAR (PolSAR) — full-polarimetric decomposition **ID:** `L1-109` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Remote Sensing — *Polarimetric scattering analysis* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** polarization decomposition map > **📡 Carrier:** radio_wave · **🌫 Noise:** speckle > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554198 --- ## 🧠 1. Introduction **Polarimetric SAR (PolSAR) — full-polarimetric decomposition** is a **linear inverse problem** whose unknown lives in **polarization decomposition map** space, within the **Polarimetric scattering analysis** sub-domain of **Remote Sensing**. Measurements consist of radio-frequency electromagnetic waves via a **polarimetric sar** sensing mechanism. The forward operator applies, in order: L · emit · polarized chirp operator; L · scattering matrix operator; L · polarimetric decompose operator; pixel-level spatial averaging on the detector. Observations are corrupted by multiplicative speckle from coherent imaging. Existence of the recovered polarization decomposition map 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 ~= 16); polarization_crosstalk dominates the stability cliff; calibration_drift and the remaining mismatch parameters contribute higher-order bias terms. Multiplicative speckle (rayleigh amplitude / exponential intensity) 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 · emit · polarized chirp → L · scattering matrix → L · polarimetric decompose → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.polarimetric_decompose` `L.scattering_matrix` `L.emit.polarized_chirp` x · η, η ~ speckle (multiplicative) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.emit.polarized_chirp` | L · emit · polarized chirp operator | | `L.scattering_matrix` | L · scattering matrix operator | | `L.polarimetric_decompose` | L · polarimetric decompose operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Remote Sensing | | Sub domain | Polarimetric scattering analysis | | Carrier | radio_wave | | Problem class | linear_inverse | | Solution space | polarization_decomposition_map | | Noise model | speckle | | Integration axis | spatial | | Difficulty delta | 5 | | L dag | 3.8 | ## 📡 4. Measurement Model Existence of the recovered polarization decomposition map 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 ~= 16); polarization_crosstalk dominates the stability cliff; calibration_drift and the remaining mismatch parameters contribute higher-order bias terms. Multiplicative speckle (rayleigh amplitude / exponential intensity) 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:** `polsar` · **Forward operator:** `polsar_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 4096 | | W | px | 4096 | | Snr db | dB | 18 | | Pixel m | m | 5 | | Lambda cm | — | 5.6 | | Faraday rotation | — | 0 | | Calibration drift | — | 0 | | Polarization crosstalk | — | -30 | | Speckle coherence loss | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 1024 – 16384 | | W | px | 1024 – 16384 | | Snr db | dB | 0.0 – 30.0 | | Pixel m | m | 0.5 – 30 | | Lambda cm | — | 0.5 – 30 | | Faraday rotation | — | 0.0 – 30.0 | | Calibration drift | — | 0.0 – 2.0 | | Polarization crosstalk | — | -40 – -15 | | Speckle coherence loss | — | 0.0 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 22.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `320` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x48a5b959081504d2b4e5055db65c316af4b9c1244080a512937aff843a755ab3` - **Chain tx hash:** `0x8de4592585236f7b32462e51fd40c9cbb1cae1fbcc27bdba779c34898aae9af3` - **Chain block:** `41554198` --- ## File Mapping This bundle consists of: `L1-109.md`, `L1-109.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-109.md` | Source of truth — edit this | Human or LLM | | `L1-109.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 `L1-109`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-109.md).
Regenerate L1-109.json so every field matches the Markdown.
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L2-109-001 Polarimetric SAR (PolSAR) — full-polarimetric decomposition Mismatch-Only Spec

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📋 JSON metadata

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    "title": "Polarimetric SAR (PolSAR) \u2014 full-polarimetric decomposition"
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  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Polarimetric scattering analysis",
  "title": "Polarimetric SAR (PolSAR) \u2014 full-polarimetric decomposition"
}

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