SPECT-CT Fusion L1-158
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
SPECT-CT Fusion: spect ct fusion produces the measurement through a 4-node primitive DAG L.ct_attenuation_map -> L.spect_activity_map -> L.registration -> int.spatial, with spatially-projected accumulation and additive Gaussian thermal/electronic noise. Recovery is posed as a linear inverse problem that inverts the forward operator to estimate the scene-side 3D fused activity anatomy. Difficulty tier delta=3 with effective condition number kappa_eff~13; calibration-level mismatch (registration_error, patient_motion, attenuation_correction_bias) 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:
- 260
Existence of the recovered 3D fused activity anatomy 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 ~= 13); registration_error dominates the stability cliff; patient_motion and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point.
Solvability C
- Solver class:
- linear-operator + convex optimisation [Rigid-Reg, AC-OSEM] | linear-operator + deep neural prior [SPECT-CT-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