Incoherent　optical　cryptosystem　is　promising　for　its　immunity　against　coherent　noise　and　insensitivity　to　misalignment,　and　compressive　encryption　is　desirable　considering　the　increasingly　demand　on　the　exchange　of　encrypted　data　via　Internet.　In　this　paper,　we　propose　a　novel　optical　compressive　encryption　approach　with　spatially　incoherent　illumination　based　on　deep　learning　(DL)　and　space　multiplexing.　For　encryption,　the　plaintexts　are　individually　sent　to　the　scattering-imaging-based　encryption　(SIBE)　scheme　where　they　are　transformed　to　scattering　images　with　noise　appearances.　Afterwards,　these　images　are　randomly　sampled　and　then　integrated　into　a　single　package　(i.e.,　ciphertext)　by　space　multiplexing.　The　decryption　is　basically　the　inverse　of　the　encryption,　while　it　involves　an　ill-posed　problem　(i.e.,　recovering　the　noise-like　scattering　image　from　its　randomly　sampled　version).　We　demonstrated　that　such　a　problem　can　be　well　resolved　by　DL.　The　proposal　is　radically　free　from　the　cross-talk　noise　existing　in　many　current　multiple-image　encryption　schemes.　Also,　it　gets　rid　of　the　linearity　bothering　the　SIBE　and　is　hence　robust　against　the　ciphertext-only　attack　based　on　phase　retrieval　algorithm.　We　present　a　series　of　experimental　results　to　confirm　the　effectiveness　and　feasibility　of　the　proposal.　©　2023　Optica　Publishing　Group　under　the　terms　of　the　Optica　Open　Access　Publishing　Agreement.