Comparing to the original backprojection (BP) algorithm, the fast factorized backprojection algorithm accelerates enormously by dividing the synthetic aperture into many small pieces and finishes the BP integral in many stages. Numerous two-dimensional (2-D) image interpolation operations are utilized to raise accuracy. In this letter, a new factorized backprojection algorithm is proposed where no interpolation is involved. Coarse images are reconstructed and fused precisely in Cartesian coordinates. A spectrum compression method is introduced to decrease the Nyquist sampling requirement in cross-range direction for efficiency. Simulation and real-data experiments prove the validity and superiority of the proposal.