{"artifact_id":"L1-503","layer":"L1","title":"Quantitative Susceptibility Mapping (QSM)","domain":"Medical Imaging","sub_domain":"Quantitative MR susceptibility recovery (multi-physics joint inverse)","physics_fingerprint":{"L_DAG":7.4,"title":"Quantitative Susceptibility Mapping (QSM)","domain":"Medical Imaging","carrier":"radio_wave","primitives":["L.rf_excitation","L.gradient_echo","L.larmor_precession","L.maxwell_magnetostatic","L.dipole_convolution","L.phase_extract","int.spatial"],"sub_domain":"Quantitative MR susceptibility recovery (multi-physics joint inverse)","noise_model":"gaussian","problem_class":"linear_inverse","solution_space":"3D_quantitative_susceptibility","difficulty_delta":5,"integration_axis":"spatial","sensing_mechanism":"mri_gre_phase_with_maxwell_magnetostatic"},"observable_profile":{"metric":"PSNR_dB","regime":"Existence of recovered 3D quantitative susceptibility chi(r) is guaranteed within the declared Omega bounds. Uniqueness holds on the wave-cone-supported subspace; modes inside the magic-angle zero cone are recovered only through priors (MEDI L1-edge, TGV second-order, deep-prior). Stability is moderately conditioned (kappa_eff ~ 30 after wave-cone regularization) — B0_inhomogeneity and background_field_removal_error dominate the stability cliff; phase_unwrap_error and dipole_kernel_truncation contribute higher-order bias terms. Joint Hadamard well-posedness for the coupled phase-field-susceptibility forward is established by Liu, de Rochefort, Wharton, Bilgic literature 2009-2018 (see references).","secondary":"RMSE_ppm"},"size_tiers":{"center_spec":{"omega":{"H":256,"W":256,"Z":64,"SNR_dB":24,"N_echoes":6,"TE_ms_max":30.0,"TE_ms_min":5.0,"B0_field_T":3.0,"voxel_size_mm":1.0,"B0_inhomogeneity":0.0,"phase_unwrap_error":0.0,"brain_segmentation_error":0.0,"background_field_removal_error":0.0,"dipole_kernel_truncation_error":0.0},"input_format":"multi_echo_complex_gre","problem_class":"qsm","forward_operator":"qsm_joint_forward","epsilon_fn_center":"30.0"},"omega_bounds":{"H":[128,512],"W":[128,512],"Z":[32,256],"SNR_dB":[10.0,40.0],"N_echoes":[1,12],"TE_ms_max":[10.0,80.0],"TE_ms_min":[2.0,15.0],"B0_field_T":[1.5,7.0],"voxel_size_mm":[0.5,2.0],"B0_inhomogeneity":[0.0,0.3],"phase_unwrap_error":[0.0,0.3],"brain_segmentation_error":[0.0,0.2],"background_field_removal_error":[0.0,0.3],"dipole_kernel_truncation_error":[0.0,0.2]},"epsilon_bounds":{"psnr_db":[10.0,50.0]},"allowed_problem_classes":["qsm","qsm_single_orientation","qsm_multi_orientation_cosmos"],"allowed_omega_dimensions":["H","W","Z","N_echoes","TE_ms_min","TE_ms_max","B0_field_T","SNR_dB","voxel_size_mm","B0_inhomogeneity","brain_segmentation_error","phase_unwrap_error","dipole_kernel_truncation_error","background_field_removal_error"],"allowed_forward_operators":["qsm_joint_forward","qsm_single_echo_forward","qsm_multi_orientation_forward"]},"hardness_fn":{"type":"epsilon_fn","delta":5,"kappa":240,"metric":"PSNR_dB"},"initiator_dataset":[{"name":"primary","weight":1.0,"ipfs_cid":null,"license_hash":null}],"status":"testnet","staked_pwm":0.0,"chain_hash":"0x5484b9c5e5758b3aa4e5899dc46d6d1ae08db76a89c897222e2c1d8d7f974782","chain_tx_hash":"0xbc7817f39f0ec56bc0fc58a6a8a6d43afe92dda05c0fd3d923f880b08273214a","chain_block":41553359}