© Springer Nature Switzerland AG 2018. We propose a neural approach for fusing an arbitrary-length burst of photographs suffering from severe camera shake and noise into a sharp and noise-free image. Our novel convolutional architecture has a simultaneous view of all frames in the burst, and by construction treats them in an order-independent manner. This enables it to effectively detect and leverage subtle cues scattered across different frames, while ensuring that each frame gets a full and equal consideration regardless of its position in the sequence. We train the network with richly varied synthetic data consisting of camera shake, realistic noise, and other common imaging defects. The method demonstrates consistent state of the art burst image restoration performance for highly degraded sequences of real-world images, and extracts accurate detail that is not discernible from any of the individual frames in isolation.