A non-iterative and non-interferometric computational imaging method to reconstruct a complex wave field called synthetic aperture imaging based on Kramers–Kronig relations (KKSAI) is reported. By collecting images through a modified microscope system with pupil modulation capability, we show that the phase and amplitude profile of the sample at pupil limited resolution can be extracted from as few as two intensity images by using Kramers–Kronig (KK) relations. It is established that as long as each subaperture’s edge crosses the pupil center, the collected raw images are mathematically analogous to off-axis holograms. This in turn allows us to adapt a recently reported KK-relations-based phase recovery framework in off-axis holography for use in KKSAI. KKSAI is non-iterative, free of parameter tuning, and applicable to a wider range of samples. Simulation and experiment results have proved that it has much lower computational burden and achieves the best reconstruction quality when compared with two existing phase imaging methods.