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In Positron Emission Tomography, there are several causes of quantitative inaccuracy, such as partial volume or spillover effects. The impact of these effects is greater when using radionuclides that have a large positron range, e.g. Ga-68 and I-124, which have been increasingly used in the clinic. We have implemented and evaluated a local projection algorithm (LPA), originally evaluated for SPECT, to compensate for both partial-volume and spillover effects in PET. This method is based on the use of a high-resolution CT or MR image, co-registered with a PET image, which permits a high-resolution segmentation of a few tissues within a volume of interest (VOI) centered on a region within which tissue-activity values need to be estimated. The additional boundary information is used to obtain improved activity estimates for each tissue within the VOI, by solving a simple inversion problem. We implemented this algorithm for the preclinical Argus PET/CT scanner and assessed its performance using the radionuclides F-18, Ga-68 and I-124. We also evaluated and compared the results obtained when it was applied during the iterative reconstruction, as well as after the reconstruction as a postprocessing procedure. In addition, we studied how LPA can help to reduce the 'spillover contamination', which causes inaccurate quantification of lesions in the immediate neighborhood of large, 'hot' sources. Quantification was significantly improved by using LPA, which provided more accurate ratios of lesion-to-background activity concentration for hot and cold regions. For F-18, the contrast was improved from 3.0 to 4.0 in hot lesions (when the true ratio was 4.0) and from 0.16 to 0.06 in cold lesions (true ratio = 0.0), when using the LPA postprocessing. Furthermore, activity values estimated within the VOI using LPA during reconstruction were slightly more accurate than those obtained by post-processing, while also visually improving the image contrast and uniformity within the VOI.