The　noise-like　visual　feature　of　cipher　images　produced　by　using　the　traditional　image　encryption　technology　explicitly　reflects　the　presence　of　secret　information.　To　overcome　this　issue,　a　visually　meaningful　image　encryption　algorithm　is　proposed　based　on　a　newly　designed　2D　memristive　chaotic　map,　P-tensor　product　compressive　sensing　(PTP-CS)　and　discrete　Hartley　transform　(DHT).　For　concreteness,　a　new　two-dimensional　discrete　memristive　chaotic　map　is　first　designed　to　provide　highly　unpredictable　secret　code　streams　while　maintaining　low　time　consumption.　Second,　the　threshold　processing　and　zigzag　confusion　operations　are　performed　on　the　discrete　wavelet　coefficients　of　the　plain　image　to　meet　the　prerequisites　for　effective　compression.　Third,　the　intermediate　secret　information　is　obtained　by　utilizing　PTP-CS　in　the　compression　layer.　Information　entropy　and　edge　entropy　are　employed　to　adaptively　identify　the　complex　regions　that　are　suitable　for　embedding　due　to　inconspicuous　visual　degradation　in　the　carrier　image.　Finally,　the　embedding　of　the　secret　information　in　the　DHT　domain　of　these　regions　is　accomplished.　Security　test　and　performance　analysis　confirm　that　our　algorithm　has　the　advantage　of　a　high　balance　between　the　encryption　security　and　the　decryption　recovery,　and　exhibits　excellent　performance　in　important　indicators　such　as　visual　quality,　robustness　and　timeliness.