why，Using wavelet packet noise reduction to find SNR (signal-to-noise ratio) can not get the optimal number of decomposition layers

Is SNR a criterion for judging the denoising effect? ​​I use wavelet packet denoising, the number of decomposition layers is from one layer to 5 layers, the calculated signal-to-noise ratio gradually decreases, which is too unreasonable, it keeps decreasing, how can I get the decomposition How many layers are the best denoising decomposition layers? What is the problem? PS, I use matlanb's own snr function snr (originalSignal, originalSignal-DenoisedSignal)Thank you for your answer!

Answer 1

[Vaibhav]

Hi Congmin

I understand you're wondering about using Signal-to-Noise Ratio (SNR) values to judge the denoising effectiveness in wavelet packet denoising. You've noticed a gradual decrease in SNR with different decomposition layers (from one to five).

SNR is a criterion for judging the denoising effect. However, relying solely on SNR can be misleading. SNR might decrease due to signal components being wrongly identified as noise and removed.

To gain a clearer picture, here are some suggestions:

Multi-criteria assessment: Combine SNR with other criteria like Mean Square Error (MSE) and Peak Signal-to-Noise Ratio (PSNR) using MATLAB functions like "immse" and "psnr". This provides a more comprehensive picture of denoising effectiveness.

Noise estimation: Ensure you're using an accurate noise estimation technique like "wnoisest" before denoising. Inaccurate estimates can lead to misleading SNR calculations and suboptimal results.

Wavelet selection: Experiment with different wavelet functions. Choosing the right wavelet can significantly improve denoising performance.

You can refer to the following MathWorks documentation links to know more about "immse", "psnr" and "wnoisest" respectively:

https://www.mathworks.com/help/images/ref/immse.html?s_tid=doc_ta

https://www.mathworks.com/help/images/ref/psnr.html?searchHighlight=psnr&s_tid=srchtitle_support_results_1_psnr

https://www.mathworks.com/help/wavelet/ref/wnoisest.html?searchHighlight=wnoisest&s_tid=srchtitle_support_results_1_wnoisest

Hope this helps!