In　order　to　reduce　the　amount　of　video　data　that　needs　to　be　acquired　greatly,　state-of-the-art　of　the　image-based　rendering　(IBR)　method　maps　the　dense　viewpoint　information　into　the　original　signal　in　the　compressed　sensing　frame　and　utilizes　sparse　viewpoint　images　as　random　measurement　information.　However,　the　low-dimensional　measurement　signals　are　linearly　combined　using　all　of　the　dense　viewpoint　information,　and　the　sparse　viewpoint　images　only　originate　from　partial　viewpoint　information,　which　results　in　the　images　acquired　by　the　sparse　viewpoints　are　inconsistent　with　the　low-dimensional　measurement　signal.　A　sparse　viewpoint　measurement　matrix　is　proposed,　and　an　interval　sampling　matrix　is　used　to　align　the　sampling　positions　between　the　measured　values　and　sparse　viewpoint　image　information.　Then,　we　constrain　the　sensing　matrix,　which　consists　of　the　measurement　matrix　and　basis　function,　to　satisfy　the　restricted　isometry　property　as　much　as　possible.　Finally,　the　unique　solution　of　the　original　signal　can　be　obtained.　The　simulation　results　show　that　compared　with　conventional　methods,　the　proposed　method　improves　the　subjective　and　objective　quality　for　scene　reconstruction　with　different　levels　of　complexity.　Copyright　©　2021　Acta　Automatica　Sinica.　All　rights　reserved.