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Fig. 15 | EJNMMI Physics

Fig. 15

From: Algorithms for joint activity–attenuation estimation from positron emission tomography scatter

Fig. 15

a Classification of image-space voxels j contributing to a measurement on SOR i; in terms of \(\smash {a^{{i}}_{{j}}}\) (contribution through scattering), \(\smash {\sum _{s} k^{{i}}_{s,{j}}}\) (contribution through attenuation) and \(\smash {k^{{i}}_{s,{j}}}\) (contribution through attenuation specifically along broken LOR (i,s)). b Comparison of different slices of \(\underline {\boldsymbol {K}}\): \(\smash {k^{i}_{169,t}}\) as a function of t (top) and \(\smash {k^{{i}}_{s,169} }\) as a function of s (bottom) for i=(ds,dn,E)=(24,8,5). Top: with the endpoints of the SOR i at the bottom left (detector 8) and bottom right (detector 24), and a scattering location in a central voxel (index 169, see Fig. 4), \(\smash { k^{{i}}_{169,t} }\) represents the attenuation weights of voxels t along the (one) broken LOR (i,s=169). Bottom: by contrast, \(\smash {k^{{i}}_{s,169}}\) shows the attenuation weights of the (one) voxel t=169 along various, different broken LORs (i,s) with the same endpoints, but different scattering locations s

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