A system and method for projection number and radiation dose reduction in tomographic imaging that creates a three dimensional cross sectional image of an object by the reconstruction of its projections. Images of a superior quality can be obtained with a fewer number projections than seen with conventional methods by reconstruction of projections that have been pre-processed and preferably placed in the Fourier domain with a Fractional Fourier Transform (FrFT) or forward Pseudo-polar Fast Fourier transform (PPFFT). The projections are iteratively refined through formulation of a constrained optimization problem with constraints in object space and Fourier space preferably solved with a gradient descent algorithm incorporating a Bregman iterative regularization or a continuative regularization. By using an exact Fourier-based iterative algorithm as well as physical and mathematical constraints, convergence to a lowest-possible noise state that is also strictly consistent with the measured data can be obtained.