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As the SNR function is not commutative (meaning different argument positions will lead to different output results), it makes me confused to use it as metric evaluation.

I have this 3 signal; those are X_test, y_test, and y_pred. Those are common naming conventions for supervised learning models. So what are they for common people?

  • X_test is basically input of an ML model, which is noisy signal.
  • y_test is basically a denoised signal, which is the ground truth of clean signal.
  • y_pred is basically a denoised signal, which is a predicted clean signal by model.

enter image description here

The question is, how do I know how much the signal has been denoised? There are some combinations, but I don't know which one. Is it:

  1. SNR(X, y)
  2. SNR(y, X)
  3. SNR(y_test, y_pred)
  4. SNR(y_pred, y_test)

Sorry, I didn't define the SNR function due to being unsure of what SNR formula I should use.

If you are wondering what SNR am I being used (might be wrong), here it is:

def SNR(a, b):

  # At this point I don't know what is a or b? And which one is denoised and noised.

  # Calculate the power of the true signal
  true_signal_power = np.sum(np.square(a), axis=1)

  # Calculate the power of the noise (difference between true and predicted signals)
  noise_power = np.sum(np.square(a - b), axis=1)

  # Calculate SNR in decibels
  snr = 10 * np.log10(true_signal_power / noise_power)

  return snr
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The remaining is simply the difference between the noise signal and the clean signal. You can define 3 different SNRs here

The SNR of your original signal is

$$SNR_{original} = 10\log_{10}\frac{\sum y_{test}^2}{\sum (x-y_{test})^2}$$

After the denoising the SNR is

$$SNR_{denoised} = 10\log_{10}\frac{\sum y_{test}^2}{\sum (y_{pred}-y_{test})^2}$$

The SNR improvement is then simply the difference of the two

$$SNR_{improvement} = SNR_{denoised} - SNR_{original} = 10\log_{10} \frac{\sum (x-y_{test})^2}{\sum (y_{pred}-y_{test})^2}$$

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  • $\begingroup$ Could you explain the difference between SNR improved and SNR denoised? My brain interpreted both as same, no difference. $\endgroup$ Commented Jun 15 at 16:34
  • $\begingroup$ I'm skeptical about $$SNR_{denoised}$$, it accepts y_pred and y_test. I mean, how you imply y_pred is denoised signal of y_test? I mean both of them supposed to be clean signal, there is nothing compare, CMIIW. $\endgroup$ Commented Jun 16 at 2:40

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