Learning Tomography: Non-centered projections

Why is my reconstruction so bad ?
This question often arises when the resulting image (or volume) is so disappointing... Specially when you are working with experimental projections, new artifacts and defects are appearing never met before in this series Learning Tomography where all the images are always perfect.
Thus, it is time to show some of these defects... to understand how to fix them.

Non-centered Projections

One of the first problem is the rotation center... because in tomography, we assume that the center of rotation − used during the back-projection process − is superimposed to the image center.
Why is it so important? Just look at this example, the sinogram of Fig. 1 was calculated from a 256x256 8-bit Lena with a rotation center located at (136, 132) corresponding to her right eye (the modified script is here [Link]). That means that during the sinogram computation, Lena is rotated about her right eye and then vertically projected.

Fig.1: Sinogram of Lena (256x256 8-bit image) calculated with a center of rotation (136, 132) roughly corresponding to her right eye. This sinogram was filtered with a ramp filter.

Now, from this sinogram (Fig.1), run the script backProjImproved.js [Link] to compute the image of Fig.2 unveiling .... a crying Lena !!

Fig.2: Reconstruction with the script backProjImproved.js. In this script, we assume that the center of rotation is located at (128,128).

The Lena is distorted because each row of the sinogram was back-projected yielding a 256x256 temporary image and rotated about its center (128,128). This distortion is only due to the discrepancy between the rotation centers used during the sinogram (136,132) and the back-projection (128,128).

This defect is characterized by a specific pattern.: Each dotted feature in the image (the eyes, for example) appears as an arc. Thus, if you see this artifact, a pre-processing of your projections is required to align them along a vertical centered axis (in the case of a equatorial collection scheme).


Hope this helps and thank you for reading these lines.

>> Next: Playing with dots

Other crazybiocomputing posts

Further readings are available in ...

• Learning Tomography Series  [Link]
• Image Processing TOC [Link]