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.