Spectral Factorization by Radon transform
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Hello,
I am interested in doing a spectral factorization of a 2D signal. To get that I am using the radom transform (radon.m and iradon.m matlab functions) to use a 1D spectral factorization instead of a 2D. I have read in the literature that you can do the radon transform, make the 1D spectral factorization to all the projections and do the iradon (tha radon transform back) to get the same result as if you had made a 2D spectral factorization.
The problem is that I am not getting very good results and I do not know if I am doing something wrong (the spectral factorization 1D function is totally checked).
Thanks in advance
답변 (3개)
Matt J
2012년 12월 14일
편집: Matt J
2012년 12월 14일
I'm assuming that by "spectral factorization" you mean "Fourier Transform".
Then, no. IRADON wouldn't be involved. The 1D spectra form the radial cross-sections of the 2D spectra through the 2D frequency origin. In other words, they give you samples of the 2D spectra on a polar coordinate grid. You would use interp2 or something to interpolate back to Cartesian coordinates.
The result will be influenced by interpolation artefacts as well as artefacts in the output of RADON, which uses a rather crude algorithm, unfortunately.
Why exactly are you interested in doing it this way? It's much more efficient and accurate to do a 2D Fourier transform directly.
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Peter
2012년 12월 17일
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Matt J
2012년 12월 17일
편집: Matt J
2012년 12월 17일
FYI, the "Answers" in these threads are not meant as a means of dialogue. You should respond to other peoples' Answers using Comments. If you have follow-up to your original Question, you can post that as a Comment to that Question, like Sean has done.
Aside from that, neither the problem you are attacking, nor the technique used to solve it look like common knowledge. It might help if you post some links to relevant sources. In particular an impulse response that "satisfes a given auto-correlation" seems like weird lingo to me.
It could be that the artifacts you are seeing are purely due to under-sampling. Maybe if you applied radon over more angles, it would improve the result. As I also mentioned earlier, RADON uses a rather crude algorithm. The Siddon algorithm, e.g., as used here
might give better results.
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