Dual-Energy X-ray Absorptiometry (DEXA) L1-037
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
Dual-Energy X-ray Absorptiometry (DEXA): dual energy xray produces the measurement through a 4-node primitive DAG L.xray_source_dual -> L.beer_lambert -> L.two_material_decompose -> int.spatial, with spatially-projected accumulation and photon-shot-noise-limited (Poisson counting). Recovery is posed as a linear inverse problem that inverts the forward operator to estimate the scene-side 2D bone mineral density. Difficulty tier delta=3 with effective condition number kappa_eff~10; calibration-level mismatch (beam_hardening, patient_alignment, fat_fraction_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:
- 200
Existence of the recovered 2D bone mineral density 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 ~= 10); beam_hardening dominates the stability cliff; patient_alignment and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) 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 [Dual-Energy-LS] | iterative projection (ADMM / GAP) + optimisation [Iterative-Dual] | linear-operator + deep neural prior [DEXA-Net]
- Convergence rate q:
- 2
- Complexity:
- O(H * W * log(...)) per iteration; learned variants: O(H W Z * F_theta_cost) per forward pass