Trajectory　reconstruction　aims　to　recover　the　missing　position　of　moving　objects　in　a　given　video,　which　is　important　for　predicting　the　behavior　of　motion　objects.　The　existing　trajectory　estimations　focus　on　frame-by-frame　object　detection　and　tracking.　However,　these　methods　cannot　handle　complex　situations　such　as　mutual　occlusion　of　multiple　objects.　To　solve　the　posed　problem,　we　propose　a　novel　motion　trajectory　reconstruction　based　on　object　matching　and　graph　signal　processing.　Specifically,　we　first　extract　the　features　of　objects　by　detection　and　then　perform　object　matching　via　similarity　scores.　The　gradient　graph　Laplacian　regularizer　is　used　to　interpolate　the　missing　trajectory　signals.　We　can　effectively　reconstruct　motion　trajectory　signals　with　a　higher　sampling　ratio　of　video　frames.　We　do　not　require　knowledge　of　the　underlying　motion　information　and　can　accurately　estimate　the　position　in　occlusion.　Experimental　results　show　that　the　quality　of　our　trajectory　reconstruction　outperforms　other　competing　algorithms.