Diffusion MRI (DWI / DTI / HARDI) L1-045
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
Diffusion MRI (DWI / DTI / HARDI): mri fourier encoding produces the measurement through a 4-node primitive DAG L.rf_excitation -> L.diffusion_gradient -> L.gradient_encoding -> int.angular, 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 4D diffusion tensor or ODF. Difficulty tier delta=5 with effective condition number kappa_eff~18; calibration-level mismatch (eddy_currents, motion, B0_distortion) 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 4D diffusion tensor or ODF 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 ~= 18); eddy_currents dominates the stability cliff; motion 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 [DTI-LLS, HARDI-CSD] | linear-operator + deep neural prior [dMRI-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