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this is part three of the lecture entitled linear systems and their diagonalization where ill be going into the basics of pet imaging the data acquisition back projection synograms list mode data and the example of convolution this is just a motivating example for better understanding of linear systems and diagonalization so in pet imaging we have for example an f-18 labeled compound such as fluorodeoxyglucose thats injected into the subject under study we know that the fluorine 18 will decay to oxygenating with release of two back-to-back photon pairs which arise from annihilation of the positron with any surrounding electron and so this is just by using e equals m c squared just the conversion of the rest mass energy of the electron and the positron which is emitted from the f18 which is a positron emitter get two back-to-back photon pairs and those back-to-back photon pairs are detected by a pet scanner and so here im just depicting those various back-to-back photon pairs coming