A single exposure superresolution (SR) restoration algorithm for an optical sparse aperture (OSA) imaging system based on random convolution is proposed. The low-resolution image from the OSA system is restored by adding a set of incoherent measurements taken using random convolution architecture, in which there is a random phase mask in the Fourier plane and a random amplitude mask in the image plane in the conventional optical 4f system. Both masks are generated by chaotic maps. The simulation results show that this algorithm can effectively recover the images degraded by both optical diffraction effect and geometrical limited resolution under noisy and aberrated conditions. The spatial resolution gain factor is above 2.82 without subsampling and 1.26 with subsampling. Moreover, it can obtain a better restoration quality than traditional algorithms by optimizing the initial conditions of chaotic maps.