A　visually　meaningful　image　encryption　algorithm　is　presented.　More　specifically,　a　strategy　of　M-ary　decomposition　is　first　presented　to　be　used　to　represent　a　positive　integer　in　multi　base.　Then　the　concept　of　virtual　bits　is　presented　and　the　relationship　between　it　and　the　M-ary　decomposition　is　discussed.　Based　on　the　M-ary　decomposition　strategy,　a　non-standard　image　pre-encryption　algorithm　is　proposed　where　each　pixel　value　of　the　pre-encrypted　image　is　limited　to　a　specified　range　thus　saving　a　small　amount　of　virtual　bits　which　can　also　be　used　to　improve　the　visual　quality　of　cipher　images.　A　Generalized　Embedding　Model　is　proposed,　where　the　Generalized-LSB　(G-LSB)　method　is　used　to　embed　virtual　bits　into　the　host　domain　and　an　error-correcting　strategy　is　also　presented.　The　optimal　static　virtual　embedded　bits　(SVEB)　are　found　and　a　set　of　rules　for　dynamic　virtual　embedded　bits　(DVEB)　are　constructed.　Experimental　simulations　show　that　the　visual　quality　of　cipher　images　is　better　than　that　using　existing　visually　meaningful　image　encryption　algorithms.　(c)　2021　Elsevier　Inc.　All　rights　reserved.