Lattice Light Sheet Microscopy (LLSM) — Bessel-lattice 3D imaging L1-020
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
Lattice Light Sheet Microscopy (LLSM) — Bessel-lattice 3D imaging: lattice illumination produces the measurement through a 4-node primitive DAG L.illumination.lattice -> K.psf.detection -> S.scan.axial -> int.temporal, with axial/z-step integration and Poisson signal noise + Gaussian read noise. Recovery is posed as a linear inverse problem that inverts the forward operator to estimate the scene-side 3D intensity. Difficulty tier delta=5 with effective condition number kappa_eff~18; calibration-level mismatch (lattice_registration, dithering_phase_error, sample_induced_aberration) 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:
- 360
Existence of the recovered 3D intensity 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 ~= 18); lattice_registration dominates the stability cliff; dithering_phase_error and the remaining mismatch parameters contribute higher-order bias terms. Poisson signal noise + gaussian read 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:
- iterative maximum-likelihood (Richardson-Lucy class) [Richardson-Lucy-LLSM] | linear-operator + convex optimisation [Multi-view-LLSM] | linear-operator + deep neural prior [CARE-LLSM]
- Convergence rate q:
- 2
- Complexity:
- O(H * W * Z * log(...)) per iteration; learned variants: O(H W Z * F_theta_cost) per forward pass