Based on incoherent optical synthetic aperture, a super-resolution reconstruction method is proposed with pixel-wise phase correlation superposition and sparse a priori constraints deconvolution. A "full spatial-frequency" image is synthesized from multiview low resolution images captured from successive exposures of a single focus plane array with shift-motion over a short range. Owing to a displacement matrix of 1/30th pixel accuracy and high-order differential L1 norm sparse regularization, the experimental results show that this approach achieves a state-of-the-art result with a resolution gain factor of about 3.0 times. It is demonstrated theoretically and experimentally to be a good and practical solution to improve spatial resolution beyond the resolving power limitation of conventional imaging systems and at low cost.