A Deep Learning and Fast Wavelet Transform-Based Hybrid Approach for Denoising of PPG Signals
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Bibliographic record
Abstract
This letter presents a novel hybrid method that leverages deep learning to exploit the multiresolution analysis capability of the wavelets, in order to denoise a photoplethysmography (PPG) signal. Under the proposed method, a noisy PPG sequence of length <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> is first decomposed into <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L$</tex-math></inline-formula> detailed coefficients using the fast wavelet transform (FWT). Then, the clean PPG sequence is reconstructed with the help of a custom feedforward neural network (FFNN) that provides the binary weights for each of the wavelet subsignals outputted by the inverse-FWT block. This way, all those subsignals which correspond to noise or artefacts are discarded during reconstruction. The FFNN is trained on the Beth Israel Deaconess Medical Center dataset and a custom video-PPG dataset, whereby we compute the mean squared-error (MSE) between the denoised sequence and the reference clean PPG signal, and compute the gradient of the MSE for the back-propagation. Simulation results reveal that our proposed method reduces the MSE of the PPG signal significantly (compared to the MSE of the original noisy PPG signal): by 56.40% for Gaussian noise, by 64.01% for Poisson noise, 46.02% for uniform noise, and by 72.36% for salt-and-pepper noise (with “db10” mother wavelet).
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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