Difference of CGLS and FDK

[Bruce-WangGF]

I used both iterative and FDK methods for reconstruction. The iterative method performs somewhat better than FDK. Is this because, in my actual geometry, the detector and the source are not orthogonal? Could there be other possible issues? Thanks.

[AnderBiguri]

Heya @Bruce-WangGF .
Most if my research career, including releasing Tigre is based in the foundation that Iterative methods perform better than fdk, so I don't see any issue here 😉.

Tip: do display CT images in the same color ranges to compare them better, don't let your visualization method chose for you.

[Bruce-WangGF]

@AnderBiguri Thanks! I have another question: In TIGRE’s FDK, is it assumed by default that the X-ray source and detector are orthogonal? In my actual geometry, the detector is mounted horizontally, and the detector center is not on the same perpendicular line as the source. In other words, the source–detector line is tilted relative to the object—this is a laminography setup. In this case, how should I configure my detector setup? Are there any issues or demos that discuss this?

[AnderBiguri]

For all algorithms, the geometry definition is the only thing needed to tell Tigre the scanner settings, nothing else. This does not change regardless of the algorithm being used. Inddee by default Tigre assumes circular scanning, but you can then change this to any possible geometry by modifying the geometry parameters appropriately.

That said, FDK is an algorithm that mathematically is only defined for a standard circular scan. Some approximation for non circular are implemented in Tigre of course, but its an algorithm that is very well known to fail in non circular trajectories. This is something you can read about in most laminography papers, I believe.

[Bruce-WangGF]

Thank you for your help, I will try to vary the settings.

[AnderBiguri]

Just to be clear: the geometry must be correct to get a valid reconstruction. Any minor change in the geometry definition from the real measurements will cause major errors in reconstruction.

[sanchalitorpe-source]

To add a bit of clarification for future readers:

• The difference in quality between CGLS (or other iterative methods) and FDK is expected. Iterative methods generally outperform FDK, especially in noisy, sparse-view, or non-ideal geometries.
• In TIGRE, the same geometry definition is used by all algorithms. There is no separate “FDK geometry” or “iterative geometry”.
• However, FDK is only mathematically exact for standard circular CBCT trajectories with a source–detector pair orthogonal to the rotation axis.
• For tilted source–detector configurations (e.g. laminography), FDK becomes an approximation and typically produces characteristic artifacts or loss of resolution, while iterative methods remain applicable.

Therefore, if the geometry is correctly defined and the scan is non-circular or tilted, the observed improvement with CGLS over FDK is expected and not an error in TIGRE.