Photoacoustic Tomography (PAT) L1-041
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
Photoacoustic Tomography (PAT): photoacoustic pa produces the measurement through a 4-node primitive DAG L.laser_pulse_excite -> L.thermoacoustic_generation -> D.ultrasound_array -> int.temporal, with multi-angle tomographic integration and additive Gaussian thermal/electronic noise. Recovery is posed as a non-convex inverse problem that inverts the forward operator to estimate the scene-side 3D optical absorption. Difficulty tier delta=5 with effective condition number kappa_eff~22; calibration-level mismatch (sound_speed_heterogeneity, limited_view_geometry, laser_fluence_variation) 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:
- 440
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.
Solvability C
- Solver class:
- linear-operator + convex optimisation [UBP, Model-Based-PA] | linear-operator + deep neural prior [PA-Net]
- Convergence rate q:
- 2
- Complexity:
- O(H * W * Z * log(...)) per iteration; learned variants: O(H W Z * F_theta_cost) per forward pass