Reconstructing under-sampled PCT data includes obtaining under-sampled scan data of a subject-under-test, the object scan performed on a phase contrast computed tomography (PCT) system, performing a regularized Fourier analysis on the under-sampled scan data, correcting for one or more PCT system contributions to the under-sampled scan data by dividing the computed Fourier coefficients by Fourier coefficients representative of the one or more PCT system contributions, obtaining at least one of an absorption sinogram, a differential phase sinogram, and a dark field sinogram from the corrected Fourier coefficients, and performing tomographic reconstruction on the obtained absorption sinogram, the obtained differential phase sinogram, and the obtained dark field sinogram. A system and non-transitory computer readable medium are also disclosed.