@aneps: Just process every row (or column, depending on the symmetry axis in your system) separatey. For example, you can call the abel_inversion function 100 times for the 100 rows/colmuns, using a simple loop.

Could you please specify what exactly you mean with "masked" ? (In any case, your data has to be smooth enough to comply with the general constraints of the Abel problem.)

Hi Laurel,
if the symmetry axis is in the center of your image, the image has to be "cut in half" for Abel processing, i.e. the left and right half are calculated independently. Please remember to use something like fliplr for the left half, so that the first element of the input vector corresponds to the center of the original image.
In your case, an input vector therefore seems to contain only 64 data points. That is not much - I am not sure how well the algorithm will perform in this case.
If are still not sure whether you use the function correctly , you can send a sample image to killer@physik.uni-greifswald.de and I will take a look.
Cheers, Carsten

Recently, the journal (Zeitschrift für Naturforschung) has been digitalized. The paper on Abel inversion can be found on page 639 at

http://www.znaturforsch.com/aa/v46a/c46a.htm

1. Actually, noise is accounted for by using a finite number of cos-expansions. The less expansions you use, the more noise is filtered out (real physical information is of course neglected on the same scale as the noise, so you shouldn't use a too little number of expansion.)

2. You are right, center shift is not included in this code.

It is not necessary to figure out a function. Just use a row of your image (with the symmetry axis at the first element of the vector) as the first input of the main function ("h").

(the code works numerically (not analytically), e.g. the polynomial sample function in GENERATE_TEST_DATA is also discretized onto a grid and is not treated as an analytical function)

@aneps: Just process every row (or column, depending on the symmetry axis in your system) separatey. For example, you can call the abel_inversion function 100 times for the 100 rows/colmuns, using a simple loop.

My data input (H) is a colormap; a matrix of size 100 x 100. When I tried to use this program to perform inverse Abel transform it shows error : "Error using .*
Matrix dimensions must agree" .

I understand the input data set should be 1 X N matrix. How can I use this program in my case where I have an intensity map of mxn matrix (mine is 100x100)? Thank you.

Whenever i mask the data i have does not start from the axis symmetric center but at a position of some pixels off from the center. How to use abel inversion in this case? Please suggest some references.

Could you please specify what exactly you mean with "masked" ? (In any case, your data has to be smooth enough to comply with the general constraints of the Abel problem.)

I am using the same code for abel inversion of the axis symmetric data. I have a masked region at the center. Abel inversion is giving me a wrong values if i have a mask. What should i do to make the code work? please send me some references if u have any.

@aneps: Just process every row (or column, depending on the symmetry axis in your system) separatey. For example, you can call the abel_inversion function 100 times for the 100 rows/colmuns, using a simple loop.

Comment only

06 Nov 2014

Abel Inversion Algorithm
Fourier-based reconstruction of an unknown radial distribution assuming cylindrical symmetry.

My data input (H) is a colormap; a matrix of size 100 x 100. When I tried to use this program to perform inverse Abel transform it shows error : "Error using .*
Matrix dimensions must agree" .
I understand the input data set should be 1 X N matrix. How can I use this program in my case where I have an intensity map of mxn matrix (mine is 100x100)? Thank you.

Comment only

20 Oct 2014

Abel Inversion Algorithm
Fourier-based reconstruction of an unknown radial distribution assuming cylindrical symmetry.

Whenever i mask the data i have does not start from the axis symmetric center but at a position of some pixels off from the center. How to use abel inversion in this case? Please suggest some references.

Comment only

20 Oct 2014

Abel Inversion Algorithm
Fourier-based reconstruction of an unknown radial distribution assuming cylindrical symmetry.

Could you please specify what exactly you mean with "masked" ? (In any case, your data has to be smooth enough to comply with the general constraints of the Abel problem.)

Comment only

18 Oct 2014

Abel Inversion Algorithm
Fourier-based reconstruction of an unknown radial distribution assuming cylindrical symmetry.

I am using the same code for abel inversion of the axis symmetric data. I have a masked region at the center. Abel inversion is giving me a wrong values if i have a mask. What should i do to make the code work? please send me some references if u have any.

Comment only