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Positron range blurring can be removed from PET projection data by Fourier deconvolution. The method uses previously measured positron range spread functions whose 'cusp like' shape retains some of the higher spatial frequencey 'iformation. Although the deconvolution process amplifies the statistical noise, especially for for narrow projection bins and for isotopes with high positron energy, it can significantly improve the ability to estimate the amount of positron activity in each region of quantitation.
Stephen E. Derenzo (Wed,) studied this question.