multi-pag (sa-delta/beta calculation)#

../../../_images/sadeltabeta.png

Behavior#

This widget is used to compute the optimal \(\frac{\delta}{\beta}\) value for Paganin filtering.

It runs a series of slice reconstructions for a set of \(\frac{\delta}{\beta}\) values and computes a score for each slice (details below).

If the autofocus is locked, it will automatically select the \(\frac{\delta}{\beta}\) value that generates the highest score.

If a center of rotation has already been computed upstream (from the “axis” or “saaxis” widgets), it will be used for the reconstruction.

To speed up reconstructions, you can increase the “horizontal binning” in the Nabu properties (in the reconstruction settings tab) under the binning and subsampling section.

../../../_images/nabu_settings1.png

Score calculation#

Currently, there are two ways of computing a \(\frac{\delta}{\beta}\) reconstruction score (the same methods used for saaxis). These methods can be set in the “results” tab:

  • Standard deviation: For readability, we multiply the score by 100.

  • Total variation, calculated by the formula:

    \[tv = \sum{\sqrt{\nabla_{x}^2 + \nabla_{y}^2}}\]

    To avoid very low score values, we divide by 10e5.

  • 1 / Standard deviation

  • 1 / Total variation

The score is computed on the circumscribed square of the largest common circumscribed circle of all reconstructed slices. Using a square ROI simplifies calculations compared to a disk (for example, gradient calculations).

../../../_images/score_roi.png

Demo#

There are several video demonstrations for the sa-delta-beta widget: