A　novel　visually　secure　image　encryption　algorithm　is　proposed　by　combining　compressive　sensing　and　deep　neural　networks.　To　achieve　a　tradeoff　between　the　visual　quality　and　the　reconstruction　quality　in　different　scenarios,　a　multi-channel　sampling　network　structure　is　constructed　to　provide　different　compression　performances.　Then,　the　pre-encrypted　compressed　image　is　embedded　into　the　host　image　by　the　IWT　embedding　strategy　in　the　sampling　network.　During　the　matrix　reconstruction　process,　a　deep　reconstruction　network　is　employed　for　full　image　denoising,　significantly　reducing　the　impact　of　block　artifacts　and　resulting　in　reconstructed　images　with　higher　visual　quality.　Simulation　results　indicate　that　the　present　algorithm　can　reconstruct　images　efficiently　with　high　quality　at　very　low　sampling　rates,　while　greatly　preserving　the　advantages　of　speed　and　learning　ability　of　deep　neural　networks.　©　2023,　The　Author(s),　under　exclusive　licence　to　Springer　Science+Business　Media,　LLC,　part　of　Springer　Nature.