A　visually　meaningful　double-image　image　encryption　algorithm　is　proposed　based　on　a　fractional-order　chaotic　system　combined　with　2D　compressive　sensing　(CS).　Specifically,　in　the　pre-encryption　phase,　a　2D　discrete　wavelet　transform　(DWT)　is　performed　on　two　grayscale　images　followed　by　a　measurement　using　2D　CS.　The　measurement　matrices　are　generated　by　using　the　fractional-chaotic　system　and　Kronecker　product　(KP).　Then,　a　Zigzag　confusion　operation　is　performed　on　the　two　generated　measurement　matrices　after　quantization　to　obtain　two　secret　images.　A　new　measurement　matrix　optimization　algorithm　is　presented　to　optimize　the　high-dimensional　measurement　matrix.　In　the　embedding　phase,　a　new　repairable　embedding　algorithm　is　designed　which　combines　matrix　encoding　and　2(K)　correction　algorithm.　The　loss　of　the　carrier　image　quality　is　effectively　reduced　while　the　robustness　of　the　cipher　image　is　enhanced.　It　is　more　suitable　for　practical　applications.　Numerical　simulation　and　performance　analyses　show　that　the　average　PSNR　value　of　visually　meaningful　cipher　images　is　41.7　dB,　and　the　PSNR　value　of　the　reconstructed　image　is　1　similar　to　3　dB　higher　than　those　in　other　studies.　In　addition,　the　proposed　algorithm　is　also　superior　to　some　recently　proposed　algorithms　in　efficiency,　security,　and　robustness.