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Camera motion deblurring is an important low-level vision task for achieving better imaging quality. When a scene has outliers such as saturated pixels, the captured blurred image becomes more difficult to restore. In this paper, we propose a novel method to handle camera motion blur with outliers. We first propose an edge-aware scale-recurrent network (EASRN) to conduct deblurring. EASRN has a separate deblurring module that removes blur at multiple scales and an upsampling module that fuses different input scales. Then a salient edge detection network is proposed to supervise the training process and constraint the edges restoration. By simulating camera motion and adding various light sources, we can generate blurred images with saturation cutoff. Using the proposed data generation method, our network can learn to deal with outliers effectively. We evaluate our method on public test datasets including the GoPro dataset, Kohler's dataset and Lai's dataset. Both objective evaluation indexes and subjective visualization show that our method results in better deblurring quality than other state-of-the-art approaches.