Multiexponential reconstruction algorithm immune to false positive peak detection
Notice bibliographique
Résumé
It is widely accepted that if a forward problem is ill posed, any reconstruction algorithm must invoke prior information. However, as is shown, if the forward problem is linear and the reconstruction algorithm is representable as multiplication by a left invertible matrix, all the information in the original data will be conserved in the reconstructed spectrum. As a consequence of data conservation, the reconstructed spectrum shares many properties of the original data. These properties include that any model spectrum that is consistent with the original data will also be consistent with the reconstructed spectrum and any model spectrum that is inconsistent with the original data will also be inconsistent with the reconstructed spectrum. If, in addition, the rows of the matrix are chosen such that the reconstructed spectrum has optimal linear resolution, including minimum noise, a useful reconstruction algorithm can be produced. As a consequence, the algorithm will use no prior information and is immune to false positive peak detection caused by unreliable prior information. This formalism was used to design a multiexponential reconstruction algorithm that is useful when reliable prior information is not available. As an example of the application of the data conserving multiexponential reconstruction algorithm, it was applied to both simulated and in vivo T2 decays from white matter in the human brain. There are multiple reports in the literature of a detection of a small but distinct “myelin water” peak, in addition to the main peak, in relaxation spectra reconstructed from the in vivo T2 decays. Applying the algorithm to both simulated and in vivo T2 decays for signal to noise ratio of about 1000 yielded spectra with a main peak but with only a low shoulder in place of the myelin peak. Because of the limited resolution available without the use of prior information, these results indicated that the T2 decays are both consistent with the existence and nonexistence of a myelin peak distinct from the main peak. This neutral conclusion was confirmed by finding spectra that were as consistent with the T2 decays as those containing a myelin peak but which had low shoulders of a main peak in place of myelin peaks. Also, as would be expected given their comparable consistency with the decays, the spectra without the myelin peaks had comparable probability densities to those with myelin peaks. Therefore, the data conserving multiexponential reconstruction algorithm confirmed the existence of the main peak in white matter relaxation spectra without the use of prior information but demonstrated that the existence of a myelin peak distinct from the main peak depends on the choice of prior information.
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Prédiction distillée sur la base complète
Imitation des enseignantsNi prévalence calibrée, ni vérité terrain. Validation humaine à venir. Apprise à partir de 10 348 étiquettes directes de Codex et de 10 348 étiquettes directes de Gemma. Le mode candidate est l'union des têtes enseignantes seuillées; le consensus est leur intersection. Ces sorties portent le statut machine_predicted_unvalidated et ne sont ni des étiquettes humaines ni des étiquettes directes de modèles de pointe.
Scores Codex et Gemma par catégorie
| Catégorie | Codex | Gemma |
|---|---|---|
| Métarecherche | 0,000 | 0,000 |
| Méta-épidémiologie (sens strict) | 0,000 | 0,000 |
| Méta-épidémiologie (sens large) | 0,000 | 0,000 |
| Bibliométrie | 0,000 | 0,001 |
| Études des sciences et des technologies | 0,000 | 0,000 |
| Communication savante | 0,000 | 0,000 |
| Science ouverte | 0,000 | 0,000 |
| Intégrité de la recherche | 0,000 | 0,000 |
| Charge utile insuffisante (le modèle a refusé de juger) | 0,000 | 0,000 |
Scores machine (provisoires)
Les deux têtes enseignantes du modèle étudiant, lues sur ce travail. Un score ordonne la base pour la relecture; il n'affirme jamais une catégorie, et le statut de validation accompagne chaque rangée tel quel.
Scores de référence d'un modèle non mature (critères de maturité non atteints, 7 itérations). Un score ordonne; il n'affirme jamais une catégorie.
score_only:v0-immature-baseline · tel quel depuis la passe de notation : score_only signifie que le nombre peut ordonner les travaux, et qu'aucune étiquette de catégorie n'en découleClassification
machine, non validéePrédiction automatique; un appel candidat d’une seule tête enseignante, pas un consensus.
Le détail, modèle par modèle et score par score, se trouve en fin de page sous « Comment cette classification a été obtenue ».