Due　to　the　lack　of　paired　data,　the　training　of　image　reflection　removal　relies　heavily　on　synthesizing　reflection　images.　However,　existing　methods　model　reflection　as　a　linear　combination　model,　which　cannot　fully　simulate　the　real-world　scenarios.　In　this　paper,　we　inject　non-linearity　into　reflection　removal　from　two　aspects.　First,　instead　of　synthesizing　reflection　with　a　fixed　combination　factor　or　kernel,　we　propose　to　synthesize　reflection　images　by　predicting　a　non-linear　alpha　blending　mask.　This　enables　a　free　combination　of　different　blurry　kernels,　leading　to　a　controllable　and　diverse　reflection　synthesis.　Second,　we　design　a　cascaded　network　for　reflection　removal　with　three　tasks:　Predicting　the　transmission　layer,　reflection　layer,　and　the　non-linear　alpha　blending　mask.　The　former　two　tasks　are　the　fundamental　outputs,　while　the　latter　one　being　the　side　output　of　the　network.　This　side　output,　on　the　other　hand,　making　the　training　a　closed　loop,　so　that　the　separated　transmission　and　reflection　layers　can　be　recombined　together　for　training　with　a　reconstruction　loss.　Extensive　quantitative　and　qualitative　experiments　demonstrate　the　proposed　synthesis　and　removal　approaches　outperforms　state-of-the-art　methods　on　two　standard　benchmarks,　as　well　as　in　real-world　scenarios.　©　2019　IEEE.