# Logarithmic Amplitude Spectral Subtraction

I'm diving into audio processing and I'm trying to wrap my head around spectral subtraction. I learned there are different approaches do it based on power, magnitude, oversubtraction. My task is to perform the spectral subtraction based on the logarithmic amplitude.

My question here is:
What is the difference between magnitude spectral subtraction, logarithmic amplitude spectral subtraction, and oversubtraction?

My second question:
Which method would be more efficient for feature extraction in the context of irregular speech (noise, silence, mispronunciation...etc)

Formulae

Magnitude spectral subtraction: $$\ |\hat{X}_m( \omega )| = max\{|Y_m( \omega )| - E[|D_m( \omega )|],0\}$$

Power spectral subtraction: $$\ |\hat{X}_m( \omega )|^{2} = max\{|Y_m( \omega )|^{2} - E[|D_m( \omega )|^{2}],0\}$$

Oversubtraction: $$\ |\hat{X}_m( \omega )|^{2} = max\{|Y_m( \omega )|^{2} - \alpha E[|D_m( \omega )|^{2}], \beta[|D_m( \omega )|^{2}] \}$$