how to remove incoherent but regularly-spaced noise?
Anonymous
Specifically it occurs every 24 columns of the image,
e.g. columns 24, 48, 72, 96, ....
There is also weaker noise beside this, so columns
23, 25, 47, 49, 71, 73 etc. are affected. So altogether
1/8 of the image is ruined. The noise is incoherent, but
not exactly random: it is predominantly low frequency
down the column.
So the approach tried by a colleague was to transform
each column to frequency domain and kill the low frequency
components (on the noisy columns only). Then interpolate
these from the adjacent columns with a prediction error filter.
However, this did not work as well as he expected.
Are there algorithms which can attenuate regularly spaced
but incoherent noise?
Andor
> We have images with regularly spaced noise.
> Specifically it occurs every 24 columns of the image,
> e.g. columns 24, 48, 72, 96, ....
> There is also weaker noise beside this, so columns
> 23, 25, 47, 49, 71, 73 etc. are affected. So altogether
> 1/8 of the image is ruined. The noise is incoherent, but
> not exactly random: it is predominantly low frequency
> down the column.
> So the approach tried by a colleague was to transform
> each column to frequency domain and kill the low frequency
> components (on the noisy columns only). Then interpolate
> these from the adjacent columns with a prediction error filter.
> However, this did not work as well as he expected.
Why do you first filter the column if you are going to replace them
via interpolation? I'm probably misunderstanding you.
Anycase, if you view this row-wise, interpolation via prediction
filters might work, but you need a non-linear approach to "train" the
prediction filter. You have to assume the missing pixels unknown.
> Are there algorithms which can attenuate regularly spaced
> but incoherent noise?
There is another simple approach [1] to reconstruct the periodically
missing columns that works under mild bandwidth constraints. Contact
me if you cannot access [1].
Regards,
Andor
[1] A. Bariska, "Recovering Periodically-Spaced Missing Samples,"
IEEE
Signal Process. Mag., DSP Tips and Tricks column, vol. 24, Nov. 2007.
Andor
By the way, Matlab code that implements this algorithm is available
from
http://apollo.ee.columbia.edu/spm/?i=external/tipsandtricks
Regards,
Andor
Tim Wescott
Stripping the low frequency content with a high-pass, then replacing it
with the low frequency content from adjacent columns may work -- but I'm
not sure how different what I'm suggesting is from what your colleague
was trying.
--
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com
Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" gives you just what it says.
See details at http://www.wescottdesign.com/actfes/actfes.html
Ron N.
> Anonymous wrote:
> > We have images with regularly spaced noise.
> > Specifically it occurs every 24 columns of the image,
> > e.g. columns 24, 48, 72, 96, ....
> > There is also weaker noise beside this, so columns
> > 23, 25, 47, 49, 71, 73 etc. are affected. So altogether
> > 1/8 of the image is ruined. The noise is incoherent, but
> > not exactly random: it is predominantly low frequency
> > down the column.
> > So the approach tried by a colleague was to transform
> > each column to frequency domain and kill the low frequency
> > components (on the noisy columns only). Then interpolate
> > these from the adjacent columns with a prediction error filter.
> > However, this did not work as well as he expected.
>
> Why do you first filter the column if you are going to replace them
> via interpolation? I'm probably misunderstanding you.
If the damaged columns include signal plus noise, then
strictly replacing them via interpolation throws away
all of any signal information in those columns which
might be separable from the noise.
Andor
Agreed. However, completely replacing the missing sample is simple and
works (under the bandwidth constraints). Finding some kind of scheme
to seperate the usable from the noise might be quite difficult. I
suggest using redundancy if it is available.
ImageAnalyst
>
> - Show quoted text -
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Andor:
I thought this was impressive:
http://math.berkeley.edu/~sethian/2006/Applications/ImageProcessing/noiseremoval.html
It uses level sets to do noise reduction.
It's 2D noise, not periodic, single column noise like you have but
maybe it might be useful (adaptable to your situation) in keeping the
signal and reducing the noise, unlike interpolation which the others
pointed out will throw out your signal.
Regards,
ImageAnalyst