Hyperspectral　images　(HSIs)　are　often　corrupted　by　noises　during　acquisition,　so　the　restoration　of　noisy　HSIs　is　an　essential　procedure　for　the　following　applications.　Low-rank　representation　(LRR)　gives　us　a　very　powerful　tool　to　detect　the　subspace　singularity　of　hyperspectral　data,　but　how　to　find　a　suitable　subspace　which　better　ensure　the　low-rank　property　and　how　to　build　a　more　robust　dictionary　to　fit　with　the　LRR　framework　are　still　open　problems.　Here　in　this　paper,　a　novel　LRR-based　HSI　restoration　method　by　exploiting　the　union　structure　of　spectral　space　and　with　robust　dictionary　estimation　is　proposed.　In　this　method,　the　spectral　space　is　represented　by　a　union　structure　of　several　low-rank　subspaces　according　to　different　land-covers　and　the　dictionary　is　estimated　using　the　robust　principle　component　analysis　(RPCA)　to　guarantee　the　LRR　framework　is　more　robust　with　the　corruption　noises.　Experiments　conducted　on　both　simulated　and　real　data　show　that　our　method　achieves　great　improvement　over　the　state-of-art　methods　qualitatively　and　quantitatively.　©　2017　IEEE.