The backprojection-then-filtering algorithm was applied to proton CT data to reconstruct a map of proton stopping power relative to water (RSP) in air, water and bone. Backprojections were performed along three commonly used path estimates for the proton: straight line path, cubic spline path, and most likely path. The proton CT data was obtained through simulations using the GEANT4 simulation toolkit. Two elliptical phantoms were inspected, and an accuracy of 0.2% and 0.8% was obtained for the RSP in water and bone respectively in the region of interest, while the RSP of air was significantly underestimated.