On statistical restricted isometry property of a new class of deterministic partial Fourier compressed sensing matrices
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Bibliographic record
Abstract
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this paper, a new class of partial Fourier matrices is studied for deterministic compressed sensing. A basic partial Fourier matrix is constructed by choosing the rows deterministically from the inverse discrete Fourier transform (DFT) matrix. By a column rearrangement, the matrix is represented as a concatenation of DFT-based submatrices. Then, a full or a part of columns of the concatenated matrix is used to form a K ×N sensing matrix for deterministic compressed sensing. It is shown that the sensing matrix forms a tight frame with nearly optimal coherence. Theoretically, the sensing matrix turns out to have the statistical restricted isometry property (StRIP) for unique sparse recovery guarantee.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it