Wavelet-Domain Medical Image Denoising Using Bivariate Laplacian Mixture Model
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Bibliographic record
Abstract
In this paper, we proposed novel noise reduction algorithms that can be used to enhance image quality in various medical imaging modalities such as magnetic resonance and multidetector computed tomography. The noisy captured 3-D data are first transformed by discrete complex wavelet transform. Using a nonlinear function, we model the data as the sum of the clean data plus additive Gaussian or Rayleigh noise. We use a mixture of bivariate Laplacian probability density functions for the clean data in the transformed domain. The MAP and minimum mean-squared error (MMSE) estimators allow us to efficiently reduce the noise. The employed prior distribution is mixture and bivariate, and thus accurately characterizes the heavy-tail distribution of clean images and exploits the interscale properties of wavelets coefficients. In addition, we estimate the parameters of the model using local information; as a result, the proposed denoising algorithms are spatially adaptive, i.e., the intrascale dependency of wavelets is also well exploited in the enhancement process. The proposed approach results in significant noise reduction while the introduced distortions are not noticeable as a result of accurate statistical modeling. The obtained shrinkage functions have closed form, are simple in implementation, and efficiently enhances data. Our experiments on CT images show that among our derived shrinkage functions usually BiLapGausMAP produces images with higher peak SNR. However, BiLapGausMMSE is preferred especially for CT images, which have high SNRs. Furthermore, BiLapRayMAP yields better noise reduction performance for low SNR MR datasets such as high-resolution whole heart imaging while BiLapGauMAP results in better performance in MR data with higher intrinsic SNR such as functional cine data.
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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 | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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