Taking　photos　of　digital　screens　often　produces　color-distorting　moire　patterns　caused　by　inconsistency　between　the　color　filter　array　of　cameras　and　the　sub-pixel　layout　of　screens,　which　severely　degrades　the　quality　of　photos.　Most　existing　demoireing　methods　employ　multi-stream　network　architecture　to　simultaneously　process　the　same　moire　image　with　different　resolutions,　but　they　neglect　the　complementarity　among　different　resolutions.　In　this　paper,　we　propose　a　novel　moire　removal　model　to　address　this　issue.　Unlike　the　existing　multi-stream　based　approaches,　in　this　model,　we　present　a　progressive　texture　complementation　block　to　exploit　the　complementary　information　from　different　resolutions　in　order　to　progressively　remove　moire　textures　and　restore　image　content.　Additionally,　we　propose　a　residual　moire　removal　block,　in　which　the　depthwise　separable　convolution　is　utilized　to　remove　moire　from　image　while　reducing　computation　overhead.　This　block　also　includes　a　local　color　correction　structure,　which　is　used　to　correct　color　shifts　presented　in　the　moire　images.　Experimental　results　on　two　public　datasets　show　that　our　method　outperforms　state-of-the-art　methods.　Besides,　the　quantity　of　parameters　and　FLOPs　of　our　model　are　tens　of　times　fewer　than　the　off-the-shelf　models.　Furthermore,　our　network　framework　can　adapt　well　to　another　low-level　vision　task,　rain　removal,　in　which　our　model　also　achieves　state-of-the-art　performance.　©　1991-2012　IEEE.