Polynomial Regression filter implementation

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mosa mm
mosa mm 2016-5-24
编辑： Miftah Bedru 2022-12-15
How can I implement Polynomial Regression filter for clutter filtering?
I would appreciate if you give me an example to understand it.
Best
  2 个评论
Star Strider
Star Strider 2016-5-24
Are you doing signal processing or image processing?
mosa mm
mosa mm 2016-5-24
编辑：mosa mm 2016-5-24
Thanks for your comment, it's Signal processing. I have to design an accurate high pass filter by Polynomial Regression...

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回答（3 个）

Bjorn Gustavsson
Bjorn Gustavsson 2016-5-24
First have a look at
sgolayfilt
If you need to filter images and it's not enough to apply sgolayfilt along either direction you might possibly be ably to make a version of sgolayfilt for 2-D that uses polyfitn, in the worst case you could make a function that simply loops around using polyfitn.
HTH
  1 个评论
mosa mm
mosa mm 2016-5-24
编辑：mosa mm 2016-5-24
Thanks for your comment Bjorn. I read about it and it's FIR smoothing filter (low pass)... but what I need is an accurate high pass filter.
Have you heard about The Gram–Schmidt process? maybe it's possible through this process but I don't know how....

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Star Strider
Star Strider 2016-5-25
I’m listing this as an Answer so I can find it again. If I have the opportunity to code and test it, I’ll follow up. I’m not promising anything.
A good discussion: Ground Clutter Canceling with a Regression Filter Journal of Atmospheric and Oceanic Technology October 1999.
This reference Polynomial regression filters and Calculation of time-variant Magnitude Responses are everything I can find on it.
The legendre function seems to me to be able to produce the polynomials, but I would have to know much more about it to know if it could be applied here.
There is nothing in the File Exchange, and no MATLAB code for it online.
mireirei
mireirei 2016-12-1
has anyone figured out how to implement poly reg filter? I'm looking for a file exchange source file if possible.....
  1 个评论
Miftah Bedru
Miftah Bedru 2022-10-20
编辑：Miftah Bedru 2022-12-15
I know it will be too late by the time you see this post , I myself was looking for such implementation and all what I found was papers and some bolgs ... below are best resources in terms of sample code and quick material to read :
  1. good lecture pdf and code snips here
  2. Matlab library function here
To get more detail resources just click here . Sorry for just putting links. I saw the discussion and the code are better elaborated in the link. In case the above link get broken in the futue , here I put short code segement shared to me by a good friend regarding ploy filter that uses matrxi implemntation of polynomial filter ( I am assuiming ultrasound data/signal here )
SIG = reshape(shiftdim(SIG,2),N,[]); % SIG refers a 3D signal slow-time, fast timem and channel - signal reshaped for better application of the below filter coeff.
t = linspace(0,1,N).'; %% time span between each shot along the slow time
V(:,n+1) = ones(N,1); %%% Vandermode matrix to hold orthogonla polynomilas which will be fitted to the clutters
for k = n:-1:1
V(:,k) = t.*V(:,k+1); %%
end
A = eye(N)-V*pinv(V); #### creating filtering coeffcient using the formulata y = I - b.b'
SIG = A*SIG; %%% APPLYING THE FILTER TO THE SIGNAL
SIG = reshape(permute(SIG,[3 2 1]),siz0); %%% Reshape the filtered signal for display .
It may not be the best but I am just sharing what I got while sniffing around ...

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