Polarimetric SAR (PolSAR) — full-polarimetric decomposition L1-109
Unclaimed Principle — open for contribution
This Principle is declared in the catalog but has no reference solver, no pinned dataset, and is not registered on-chain. There is no reward pool. Submitting a cert against this Principle today will record the cert for reproducibility but pay zero PWM.
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Forward model E
Polarimetric SAR (PolSAR) — full-polarimetric decomposition: polarimetric sar produces the measurement through a 4-node primitive DAG L.emit.polarized_chirp -> L.scattering_matrix -> L.polarimetric_decompose -> int.spatial, with spatially-projected accumulation and multiplicative speckle (Rayleigh amplitude / exponential intensity). Recovery is posed as a linear inverse problem that inverts the forward operator to estimate the scene-side polarization decomposition map. Difficulty tier delta=5 with effective condition number kappa_eff~16; calibration-level mismatch (polarization_crosstalk, calibration_drift, speckle_coherence_loss) sets the accuracy floor at the Omega boundary. See the forward_model field for the closed-form imaging equation.
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- true
- Stability:
- conditional
- κ:
- 320
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.
Solvability C
- Solver class:
- linear-operator + convex optimisation [Pauli-Decomp, Freeman-Durden] | linear-operator + deep neural prior [PolSAR-Net]
- Convergence rate q:
- 2
- Complexity:
- O(H * W * log(...)) per iteration; learned variants: O(H W Z * F_theta_cost) per forward pass