A　verifiable　visually　meaningful　image　encryption　algorithm　based　on　compressive　sensing　and　(t,　n)-threshold　secret　sharing　is　proposed.　Firstly,　the　plain　image　is　compressed　and　encrypted　by　2D　block　compressive　sensing　to　obtain　the　pre-encrypted　image.　During　this　process,　the　enhanced　logistic　map　and　the　enhanced　tent　map　are　used　to　generate　the　measurement　matrix　and　the　permutation　sequence,　respectively.　Secondly,　multiple　shadow　images　of　the　pre-encrypted　image　are　generated　by　using　the　(t,　n)-threshold　secret　sharing　scheme,　and　then　each　shadow　image　is　further　encrypted　by　using　the　encryption　matrix　generated　by　the　chaotic　system.　Meanwhile,　the　signatures　of　the　shadow　images　are　obtained　by　using　RSA　signature　algorithm.　Finally,　the　shadow　images　and　their　corresponding　signatures　are　embedded　into　the　carrier　image　to　generate　the　cipher　image　with　high　visual　quality　by　using　the　LSB　method.　Additionally,　the　present　algorithm　can　resist　known-plaintext　and　chosen-plaintext　attacks　by　incorporating　the　hash　value　of　the　plain　image　as　part　of　the　key.　Meanwhile,　the　use　of　2D　block　compressive　sensing　significantly　reduces　the　reconstruction　time.　Simulation　results　demonstrate　that　the　proposed　algorithm　achieves　excellent　decryption　quality　and　operational　efficiency.　©　2024　IOP　Publishing　Ltd.