We　present　a　new　self-interference　digital　holographic　approach　that　allows　single-shot　capturing　three-dimensional　intensity　distribution　of　the　spatially　incoherent　objects.　The　Fresnel　incoherent　correlation　holographic　microscopy　is　combined　with　parallel　phase-shifting　technique　to　instantaneously　obtain　spatially　multiplexed　phase-shifting　holograms.　The　compressive-sensing-based　reconstruction　algorithm　is　implemented　to　reconstruct　the　original　object　from　the　under　sampled　demultiplexed　holograms.　The　scheme　is　verified　with　simulations.　The　validity　of　the　proposed　method　is　experimentally　demonstrated　in　an　indirectly　way　by　simulating　the　use　of　specific　parallel　phase-shifting　recording　device.　(C)　2016　Elsevier　Ltd.　All　rights　reserved.