Low-rank　matrix　decomposition　with　missing　values　is　vital　in　computer　vision　and　pattern　recognition,　yet　it　presents　significant　challenges.　This　problem　can　be　viewed　as　a　separable　nonlinear　optimization,　but　traditional　methods　often　fail　to　account　for　the　coupling　between　parameters　and　the　impact　of　solution　properties　on　visual　reconstruction.　We　observe　that　such　separable　nonlinear　problems　frequently　encounters　narrow　ravines　filled　with　sharp　minima.　Classic　alternating　optimization　methods,　the　Wiberg　algorithm　and　its　variants　tend　to　linger　in　these　regions,　converging　to　sharp　minima,　thereby　slowing　convergence　and　degrading　reconstruction　quality.　This　promotes　us　to　introduce　the　Adaptive　Decoupled　Variable　Projection　algorithm　(ADVP),　which　can　adaptively　handle　the　coupling　of　parameters,　significantly　accelerate　the　convergence　rate,　and　dynamically　adjust　the　parameter　search　subspace,　helping　algorithms　avoid　these　ravines　towards　flatter　local　minima.　These　flat　minima　exhibit　robustness　against　missing　data,　noise,　and　outliers,　enhancing　the　quality　of　visual　reconstruction.　Extensive　experiments　on　synthetic　and　real　datasets　have　validated　the　efficiency　of　ADVP　and　its　superior　performance　in　visual　reconstruction.