Optical sparse-aperture system can be designed to obtain high resolution in astronomical object imaging. It is a particular array synthesized by several small filled imaging systems. A diffraction-limited incoherent imaging model is proposed for sparse-aperture systems. Under the premise that the noise of sparse-aperture system can be regarded as ergodic random noise, and is uncorrelated to the object, then an optimum image reconstruction filter is given for sparse-aperture system in a sense of mean square errors. Finally, computer simulations of imaging and image reconstruction of a specific sparse-aperture system are performed by using the model and the filter. These numerical experiments indicate that optical sparse-aperture systems can achieve almost the same resolution and image quality as an equivalent filled system.