Bayesian Wavelet-Based Image Denoising Using the Gauss–Hermite Expansion
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Bibliographic record
Abstract
The probability density functions (PDFs) of the wavelet coefficients play a key role in many wavelet-based image processing algorithms, such as denoising. The conventional PDFs usually have a limited number of parameters that are calculated from the first few moments only. Consequently, such PDFs cannot be made to fit very well with the empirical PDF of the wavelet coefficients of an image. As a result, the shrinkage function utilizing any of these density functions provides a substandard denoising performance. In order for the probabilistic model of the image wavelet coefficients to be able to incorporate an appropriate number of parameters that are dependent on the higher order moments, a PDF using a series expansion in terms of the Hermite polynomials that are orthogonal with respect to the standard Gaussian weight function, is introduced. A modification in the series function is introduced so that only a finite number of terms can be used to model the image wavelet coefficients, ensuring at the same time the resulting PDF to be non-negative. It is shown that the proposed PDF matches the empirical one better than some of the standard ones, such as the generalized Gaussian or Bessel K-form PDF. A Bayesian image denoising technique is then proposed, wherein the new PDF is exploited to statistically model the subband as well as the local neighboring image wavelet coefficients. Experimental results on several test images demonstrate that the proposed denoising method, both in the subband-adaptive and locally adaptive conditions, provides a performance better than that of most of the methods that use PDFs with limited number of parameters.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.003 | 0.000 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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