Videos captured with hand-held cameras often suffer from a significant amount of blur, mainly caused by the inevitable natural tremor of the photographers hand. In this work, we present an algorithm that removes blur due to camera shake by combining information in the Fourier domain from nearby frames in a video. The dynamic nature of typical videos with the presence of multiple moving objects and occlusions makes this problem of camera shake removal extremely challenging, in particular when low complexity is needed. Given an input video frame, we first create a consistent registered version of temporally adjacent frames. Then, the set of consistently registered frames is block-wise fused in the Fourier domain with weights depending on the Fourier spectrum magnitude. The method is motivated from the physiological fact that camera shake blur has a random nature and therefore, nearby video frames are generally blurred differently. Experiments with numerous videos recorded in the wild, along with extensive comparisons, show that the proposed algorithm achieves state-of-the-art results while at the same time being much faster than its competitors.