Help with Inverse Radon Transform

JUN ZHOU jzhou1 at metz.une.edu.au
Wed Jul 27 04:26:16 EST 1994


Hello,

I am a postgraduate student and am using techniques of image 
reconstructions from its projections for the interpretation
of potential field data. At the very begining, I created a
numerical model of a squre object with area of 7 by 7 (unit
is arbitary) which is centered at a rectangular of 61 by 21.

The image function looks like



        -------------------------------------------
        |                                         |
        |                                         |
        |               ----------                |
        |              |          |               |
        |              |          |               |
        |              |          |               |
        |               ----------                |
        |                                         |
        |                                         |
        -------------------------------------------

and I have got its 33 projections evenly distributed with in
the range of [0,180 degree], they all looks like


                          --
                         /  \
                        /    \
                        |    |
                       /      \
                      /        \
                     |          |
                    /            \
         ------------------------------------------- 
         1 2 ......28............40................66


where the number represents the number of strip, that is
there 66 parallel strips divided in each directions.

With these projections, I tried to reconstruct the image using
filtered backprojection algorithm given by Prof. G. T. Herman in
his book (Image Reconstruction from projections,....) and Dr.'s
Sheep and Logan's Fortran Program published in IEEE trans. nucl.
1977. The reconstructed image looks like


         ----------------------------------------
         |                                      |
         |-                                     |
         |     -                                |
         |-           -                         |
         |     -              -                 |
         |           -                 -        |
         |                  -                -  |
         |                           -          |
         |                                   -  |
         |                                      |
         ----------------------------------------


which is to far away from the original image. As the projections
all indicate that there are only something in the middle, I really
confused why the result of reconstruction comes out like this.

Could experts on this topic out there be kind enough to help me
with this problem?

Any enlightening instructions will be greatly appreciated.

Jun.





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