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This lecture discusses linear systems and diagonalization in the context of PET imaging. It covers data acquisition, back projection, sinograms, list mode data, and convolution as a motivating example. In PET imaging, an F-18 labeled compound like fluorodeoxyglucose is injected into the subject, leading to the emission of back-to-back photon pairs from the decay of fluorine 18 to oxygen. These photon pairs are detected by a PET scanner, illustrating the conversion of the rest mass energy of the electron and positron emitted from F-18 into photon pairs for imaging.
