Multiexponential reconstruction algorithm immune to false positive peak detection
Bibliographic record
Abstract
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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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.006 | 0.016 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".