Dictionary Learning and Sparse Signal Recovery for NonlinearCompressive Measurements
Bibliographic record
Abstract
Sparse representations and dictionary learning have been used widely in linear inverse problems, such as denoising, inpainting, deblurring, or super-resolution. However, they have been less explored for nonlinear measurements. In this talk, we present a new method for signal recovery and dictionary learning from nonlinear measurements, such as clipping (also called saturation), and quantization. Different from conventional methods, where recovering a signal from clipped and quantized measurements is often formulated as a constrained optimization problem, we propose a unified framework for signal recovery from clipped, quantized, as well as linear measurements. With a data-fidelity term that promotes consistency with the nonlinear measurement function, we generalize the linear least-squares loss function commonly used in sparse decompositions, and show that under some conditions on the measurement function, the proposed loss is convex, and continuously differentiable with a closed-form gradient, which makes it suitable for a range of optimization algorithms. This allows us to extend classical sparse decomposition algorithms to deal with nonlinear measurements. We then discuss how to learn a dictionary from the nonlinear compressive measurements, and demonstrate its improved performance for signal reconstruction, over the use of fixed dictionaries.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".