Polynomial Regression filter implementation

How can I implement Polynomial Regression filter for clutter filtering?

I would appreciate if you give me an example to understand it.

Best

[Star Strider]

Are you doing signal processing or image processing?

[mosa mm]

Thanks for your comment, it's Signal processing. I have to design an accurate high pass filter by Polynomial Regression...

Answer 1

[Bjorn Gustavsson]

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

[mosa mm]

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....

Answer 2

[Star Strider]

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.

[mosa mm]

Thanks Star for your answer, I will figure it out.

[Star Strider]

My pleasure.

Answer 3

[mireirei]

has anyone figured out how to implement poly reg filter? I'm looking for a file exchange source file if possible.....

[Miftah Bedru]

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 ...