Blind image restoration means estimating the true image from an observed degraded image, with incomplete or little prior knowledge of the blur function and the true image. Commonly, iterative or recursive methods are applied to this problem, but they are usually time-consuming, uncertain, and divergent. Focusing on a limited but significant class of point spread functions (heavy-tailed Lévy processes), a noniterative blind image restoration method is proposed, which directly estimates the point spread functions from the degraded image's Fourier amplitude and restores the image by general slow evolution of a continuation boundary. This method is based on the fast Fourier transform, so it can accomplish the blind restoration of a 512×512 image in seconds of CPU time on a current desktop platform. From several experiments on synthetic blurred images and on actual images, it is found that the quality of the restored images has been greatly improved, and many fine details are restored, by applying this method.