Neural-networks based image restoration methods tend to use low-resolution image patches for training. Although higher-resolution image patches can provide more global information, state-of-the-art methods cannot utilize them due to their huge GPU memory usage, as well as the instable training process. However, plenty of studies have shown that global information is crucial for image restoration tasks like image demosaicing and enhancing. In this work, we propose a HighEr-Resolution Network (HERN) to fully learning global information in high-resolution image patches. To achieve this, the HERN employs two parallel paths to learn image features in two different resolutions, respectively. By combining global-aware features and multi-scale features, our HERN is able to learn global information with feasible GPU memory usage. Besides, we introduce a progressive training method to solve the instability issue and accelerate model convergence. On the task of image demosaicing and enhancing, our HERN achieves state-of-the-art performance on the AIM2019 RAW to RGB mapping challenge. The source code of our implementation is available at https://github.com/MKFMIKU/RAW2RGBNet.