How wrong could we be? A new way to solve underdetermined linear equations, illustrated via computed tomography
Bibliographic record
Abstract
Too much reliance has been placed on calculating single images meeting possibly arbitrary optimization criteria.By generating a dispersion of multiple images consistent with the data, we may be able to learn how wrong we could be.Our problem is to generate a way of seeing a representative sample of all of the solutions in the hyperplane of solutions, which would be an array of images, each of which is a solution to the equations.To accomplish this, we suggest that our sampling is in a space of image basis functions, rather than directly in the hyperplane.As the number of basis functions is large, we design a selection criterion for choosing a subset that reasonably spans the space of images.First, we try a random sampling, which gives high frequency or sequency samples.Then we turn to more systematic sampling, based on the methods developed for one-pixel imaging.Some numerical experiments demonstrate that the use of basis functions as starting images for ART-like iterative algorithms may suffice to span the hyperplane of solutions, allowing choices between solutions other than simple optimization of arbitrary criteria such as minimum norm or maximum entropy, or deconvolution of the point spread function of the algorithm.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.004 | 0.013 |
| 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 | 0.006 |
| Scholarly communication | 0.003 | 0.008 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".