Spectral analysis is a general modelling approach that enables calculation of parametric images from reconstructed tracer kinetic data independent of an assumed compartmental structure. We investigated the validity of applying spectral analysis directly to projection data motivated by the advantages that: (i) the number of reconstructions is reduced by an order of magnitude and (ii) iterative reconstruction becomes practical which may improve signal-to-noise ratio (SNR). A dynamic software phantom with typical 2-[11C]thymidine kinetics was used to compare projection-based and image-based methods and to assess bias-variance trade-offs using iterative expectation maximization (EM) reconstruction. We found that the two approaches are not exactly equivalent due to properties of the non-negative least-squares algorithm. However, the differences are small (< 5%) and mainly affect parameters related to early and late time points on the impulse response function (K1 and, to a lesser extent, VD). The optimal number of EM iteration was 15-30 with up to a two-fold improvement in SNR over filtered back projection. We conclude that projection-based spectral analysis with EM reconstruction yields accurate parametric images with high SNR and has potential application to a wide range of positron emission tomography ligands.