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In traditional lucky imaging (TLI), many consecutive images of the same scene are taken with a high frame-rate camera, and all but the sharpest images are discarded before constructing the final shift-and-add image. Here we present an alternative image analysis pipeline -- The Thresher -- for these kinds of data, based on online multi-frame blind deconvolution. It makes use of all available data to obtain a best estimate of the astronomical scene in the context of reasonable computational limits; it does not require prior estimates of the point-spread functions in the images, or knowledge of point sources in the scene that could provide such estimates. Most importantly, the scene it aims to return is the optimum of a justified scalar objective based on the likelihood function. Because it uses the full set of images in the stack, The Thresher outperforms TLI in signal-to-noise; as it accounts for the individual-frame PSFs, it does this without loss of angular resolution. We demonstrate the effectiveness of our algorithm on both simulated data and real Electron-Multiplying CCD images obtained at the Danish 1.54m telescope (hosted by ESO, La Silla). We also explore the current limitations of the algorithm, and find that for the choice of image model presented here, non-linearities in flux are introduced into the returned scene. Ongoing development of the software can be viewed at https://github.com/jah1994/TheThresher.