Fig. 2.

Flowchart of TOF iterative reconstruction using the DIRECT approach. Each 3D view-grouped histo-image contains all events from a given “view” (comprising a range of azimuthal and co-polar angles). All data (d, d∼, ω, s, r) are in the same histo-image format. Forward- and back-projection operations are 3D convolutions involving proper 3D TOF resolution kernel k_v (taking into account TOF, detector, and image based resolution functions) for each view v. Modeling of the multiplicative corrections ω before or after (dashed lines) the forward-projection is discussed in Section IV. Discrepancy and Update operators (both operating in image space) are defined by a particular iterative algorithm. The DIRECT approach can be used for both view-by-view and ordered subset iterative strategies. The DIRECT approach can also be used for analytical reconstruction, utilizing just the top part of the flowchart: deposited (and pre-corrected) data are first sequentially back-projected view-by-view (confidence weighted back-projection), and the resulting image is then properly filtered (in place of the update operation). If complete data are needed, the forward-projection part of the flowchart can be used for calculation of the axially missing regions in the oblique data (similar to what is done in the 3D reprojection (3DRP) algorithm [40], [41]).