The spatially-variant back-projection point kernel function of an energy-subtraction Compton scatter camera for medical imaging

An energy-subtraction Compton scatter camera (ESCSC) was previously proposed for in-vivo 3-D imaging of radiopharmaceuticals used as bio-tracers in nuclear medicine. To further evaluate the usefulness of this ESCSC design, studies pertaining to image reconstruction are explored and presented. Generally speaking, a Compton scatter camera works on the principle that an emitted gamma ray undergoes a Compton scatter interaction in a primary detector system and then is subsequently absorbed by a secondary detector system. Using the measured interaction energies and positions, a cone surface can be backprojected which intercepts the emission space near the point of the gamma-ray emission (proximity depends on resolution). When backprojecting and linearly superposing multiple cones into a source space, calculations should include normalizing the total weight contributed by each cone as well as how the differentially intercepted area increases as you move farther away from the vertex of the cone (i.e., intercepted voxels farther away from the vertex are given less weight). Backprojected "paint-kernel profiles", based upon simulated data, are presented corresponding to point sources located at several positions (revealing the degree of spatial variance) within the ESCSC camera geometry. From these results the spatially variant point kernel function may be deduced (e.g., via 3-D interpolation) for future use in image reconstruction. Additionally, two different algorithms for backprojection are compared.