The multi-frame blind deconvolution algorithm is considered for processing astronomical speckle images when only a few frames of data are collected. It has been noted that when the speckle data contains even moderate amounts of shot noise the algorithm often converges to the trivial point solution. The convergence properties of the Knox-Thompson algorithm are well understood, however when only a few frames of data are used, the algorithm often contains false structure referred to as processing artifacts. In this paper we consider penalized blind convolution as a `clean up' for the Knox-Thompson algorithm. The utility of this combination is demonstrated images of the Jovian moon Ganymede taken on a 1.5 meter telescope.
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