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In early studies of proton computed tomography (pCT), images were reconstructed with the fast and robust filtered backprojection (FBP) algorithm. Due to multiple Coulomb scattering of the protons within the object, the straight line path assumption of FBP resulted in poor spatial resolution. In an attempt to improve spatial resolution, a formalism to predict the proton path of maximum likelihood through the image space was created. The use of these paths with the iterative algebraic reconstruction technique (ART), have shown an improvement in spatial resolution, but also an increase in image noise, resulting in poor density resolution. In this work, we propose a reconstruction method that attempts to optimize both spatial and density resolution of pCT images. The new reconstruction approach makes use of the block-iterative diagonally relaxed orthogonal projections (DROP) algorithm with an initial FBP-reconstructed image estimate. Reconstruction of Monte Carlo simulated pCT data sets of spatial and density resolution phantoms demonstrated that the combined reconstruction approach resulted in better spatial resolution than the FBP algorithm alone and better density resolution than the DROP algorithm starting from a uniform initial image estimate.