The minimal scan range for circlular objects in fan-beam geometry is well known. Parker demonstrated a nice and efficient method to reconstruct such a short scan. Furthermore, a offset detector is able to double the FOV. However, this comes at the restriction that the scan range has to be increased to 360 degrees.

In this tutorial, we investigated the minimal scan range for non-circular objects. Here we only present a short example. The full research is found the CT Meeting Paper by Herbst et. al.

The respective sources are found in package edu.stanford.rsl.tutorial.noncircularfov.

In a first step, the object is projected into sinogram space and the image is thresholded to determine which rays have to be collected to create a complete reconstruction.

Then a mask is generated that represents the current scan configuration. Here, we chose to follow the outline of the knees from the left and chose a detector size of 250 pixels.

In a next step, the sinogram is completed using the information from redundant rays that are acquired in the fan-beam geometry. The image on the right shows the completed mask.

From the completed sinogram and the complete set, the missing rays can be determined as shown on the right.

The missing information leads to artifacts in the reconstruction. The algorithm to find configurations that determine the minimal complete scan configuration is described in the above mentioned CT Meeting Paper.