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Purpose: The scattering phenomenon creates degrading effects in positronemission tomography (PET) and the corresponding events are rejectedconventionally. We have proposed a mathematical model to retrace the originalline of response of the single-scattered coincident events with the aim toincorporate such events in PET.  Methods: We have devised a new Virtual extrapolation technique based on theconcept of the probability density functions. Through which we transformed theoriginal two-parameter list mode data for the coincident photon pairs to aone-parameter data set. The procedure of random sampling and samplingdistribution - by utilizing some unique properties like a collective differenceand the length compensation - was employed in the data analysis. We studied theeffect of finite timing and energy resolution of detectors on the performanceof the proposed model.  Results: We determined the frequency of occurrence of the data valuescorresponding to real as well as fictitious scattering points { placed on thearc of a circle drawn with the constant scattering angle - to observe thehighest counts. As expected, we found the highest counts at the location ofreal scattering points. The model was evaluated for a uniform attenuatingphantom medium. The results were found impressive for the case of ideal timeand energy information, less so for the cases of finite resolutions.  Conclusions: Our work outlines a completely new approach; though, a lot moresophistication is required for its practical utility. Nonetheless, thetechnique seems promising in developing a potential approach to improve thesensitivity of PET imaging.

Virtual extrapolation technique for retracing line of response of single scattered events in positron emission tomography