Phase Unwrapping (2D modulo-2pi inversion) L1-390
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.
To claim it as a Bounty #7 contribution: open a PR adding (1) a reference solver, (2) ≥1 dataset pinned to IPFS, (3) updates to the L3 manifest with dataset CIDs. After verifier-agent triple-review, the founders' 3-of-5 multisig signs PWMRegistry.register() and the Principle becomes mineable.
Forward model E
A true phase field phi(r) in R is wrapped into [-pi, pi] by modulo-2pi projection at acquisition (e.g., InSAR, MRI phase, holography). The task is to recover phi (2-pi ambiguity per pixel) from psi = wrap(phi) under noise and phase-discontinuity ambiguity.
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- modulo constant 2pi; unique under Itoh's condition |grad phi| < pi per pixel
- Stability:
- conditional
- κ:
- 1000
Well-posed when Itoh condition holds everywhere; ill-posed around phase residues (where gradient circulation is non-zero). LS unwrap smooths but biases; branch-cut correct when cuts routed through low-coherence regions.
Solvability C
- Solver class:
- LS (direct cosine transform), branch-cut (Goldstein), min-cost-flow (PUMA), quality-guided (Itoh path), deep (PhaseNet, DeepLab-unwrap)
- Convergence rate q:
- 2
- Complexity:
- LS: O(H*W*log(H*W)) via DCT; MCF: O((H*W)^{3/2}); deep: O(H*W*C*F) single forward