3D restoration from multiresolution data acquisition with parallel-hole collimation

Planar imaging in nuclear medicine produces a 2D representation of a 3D volumic distribution as seen by an imperfect imaging system. Imperfect because the image of a point source is a spot of variable extend represented by a point spread function (PSF) which is not only space variant (the PSF varies at a given distance from the collimator), but also depth-variant which means that the PSF varies with the source-to-collimator distance. Here, the authors focused their attention on the specific coding of the 3D information resulting from the superimposition of elementary convolutions between object slices located at a given source-to-collimator distance and their corresponding PSF, assuming that the PSF are only depth-variant (identical at a given source-to-collimator distance but varying with depth). It is shown that the knowledge of the PSF variation with depth, characterizing the imaging system in use, associated with the acquisition of a set of planar images corresponding to a volumic object located at different distances from the collimator can help to restore, or more accurately, to decode the 3D information which is encoded in every planar image