3D reconstruction

In the analytical reconstruction section we summarized the fundamental equations of image reconstruction. The analytical 3D reconstructions necessitate further development to the shown techniques. The key problem of 3D inversion techniques is the lack of data caused by the scanner geometries that renders standard formulas inapplicable directly.

• A technique for filling in the missing data is given by an approximate reconstruction then we can revert to the simple expressions (3D reprojection, 3DRP)
• As the 2D slices contain enough information for a 3D reconstruction the rest of the data should only improve the signal to noise ratio. The Single Slice Rebinning technique (SSRB) projects (rebins) the oblique LoR data to transaxial slices then does the series of 2D reconstructions
• the Fourier Rebinning (FORE) technique does the SSRB rebinning step as an interpolation in the Fourier space