Noise Subtraction

"Fred Marshall" <fmarshallx@remove_the_x.acm.org> wrote in message 
news:8cednSlPmbKYWWHfRVn-og@centurytel.net...
>
> "Jon Harris" <jon99_harris7@hotmail.com> wrote in message 
> news:8ZTKe.28995$7d.6899@trnddc08...
>> "Fred Marshall" <fmarshallx@remove_the_x.acm.org> wrote in message 
>> news:sNidnezpEIdsAWbfRVn-ow@centurytel.net...
>>>
>>> <jstout@ncon.com> wrote in message 
>>> news:1123776508.188773.199810@f14g2000cwb.googlegroups.com...
>>>> My boss showed me a feature on some commercial software he wants me to
>>>> incorporate into our system.
>>>>
>>>
>>> This suggestion very much reflects *my* attitude and may not resonate with 
>>> everyone:
>>>
>>> There is no method that will remove broadband noise unless the noise in the 
>>> desired signal is identically the same as the noise to be subtracted. This 
>>> is pretty hard to do with broadband / random noise because any relative time 
>>> delays in the two noises causes them to add and not subtract.
>>
>> I would tend to disagree with this.  Using frequency domain techniques, 
>> noise, even broadband "random" noise, can be removed to the signal within 
>> reason. There are often some artifacts that result, especially if the 
>> original SNR is low and you try to remove a lot of the noise.  But within 
>> reason, this technique works quite well.
>
> Jon,
>
> Sorry if I wasn't clear.  I meant in context: I didn't mean "filter", I meant 
> "subtract".  In order to subtract broadband noise you have to have a real time 
> reference.  I think I said that can be done.

OK, I just wanted to make sure you weren't saying that broadband noise can't be 
effectively reduced.

> So, yes a "frequency domain" method called bandstop filtering will work if the 
> signal is periodic and thus amenable to bandpass filtering to remove noise. 
> This is the classical case.  In this case, a reference signal for the noise 
> isn't needed.

The spectral subtraction method described by others in this thread is better 
suited to remove broadband (constant spectrum) noise from a broadband signal. 
If either the noise or the signal is bandlimited, simple filtering can be 
effective. 

Some comments on this, coming from someone with some (but not much)
background in removing fan noise from speech recordings.

To remove stationary noise from speech, I mainly hear about three
approaches: 'spectral subtraction', 'Wiener filtering', and
'Ephraim-Malah'.   For spectral subtraction theory, I enjoyed the
article by McAulay and Malpass in IEEE Trans. on Acoustics, Speech and
Signal Processing (April 1980) and the article by Lee and Ching in the
ICSLP 2004 proceedings.  I believe M&M suggest operating on power
spectra (I mean, squared magnitudes) and L&C suggest operating on
linear spectra.  For Ephraim-Malah, journal papers from 1984-1985 were
online at http://ece.gmu.edu/~yephraim/ephraim.html last I checked.   I
don't know what the best place to start is to learn about Wiener
filtering in this context, but if you look through what's linked to at
http://www.ICSI.Berkeley.EDU/Speech/papers/gelbart ms/pointers you will
find some Wiener filter stuff as well as some stuff about other kinds
of noise reduction.

I am guessing that any of these three approaches (as well as various
others) will work as a starting point.  How well you tweak your
implementation may make more performance difference than which
theoretical approach you start with.  In the past, people have
struggled in the past with "musical noise" artifacts with noise
reduction by Wiener filtering and spectral subtraction, and evolved
some knowledge of tweaks to deal with them.  See for example:

Phil S. Whitehead, David V. Anderson, and Mark A. Clements, "Adaptive,
acoustic noise suppression for speech enhancement", ICME 2003
(www.imtc.gatech.edu/projects/technology/media/icme2003.pdf)

If I recall correctly, in

L. Arslan, A. McCree and V. Viswanathan, "New Methods for Adaptive
Noise Suppression", ICASSP 1995

the authors speculated the musical noise was caused by temporal
discontinuity in the noise suppression filter (in other words,
variations in the noise suppression filter from frame to frame).

Such discontinuity can be addressed by smoothing (low-pass filtering)
of the filter. I have access to the system described in

A. Adami, L. Burget, S. Dupont, H. Garudadri, F. Grezl, H. Hermansky,
P. Jain, S. Kajarekar, N. Morgan, and S. Sivadas "Qualcomm-ICSI-OGI
Features for ASR" ICSLP 2002

in which the Wiener filter used for noise reduction was smoothed across
both time and frequency and when I have listened to enhanced speech
from this I have never heard any musical noise.

In case you care, here are other papers that were recommended to me on
the topic of the musical noise problem:

Klaus Linhard and Heinz Klemm. Noise reduction with spectral
subtraction and median filtering for suppression of musical tones. In
Proc. of ESCA-NATO WOrkshop on Robust Speech Recognition for Unknown
Communication Channels, pages 159-162, Pont-a-Mousson, France, April
1997.

Cappe, O., "Elimination of the musical noise phenomenon with the
Ephraim and Malah noise Suppressor", IEEE Trans. on speech and audio
processing, Vol. 2, No. 2, pp345~349, April 1994.