Robust Statistics for Image Deconvolution

Abstract: We present a blind multiframe image-deconvolution method based on robust statistics. The usual shortcomings of iterative optimization of the likelihood function are alleviated by minimizing the M-scale of the residuals, which achieves more uniform convergence across the image. We focus on the deconvolution of astronomical images, which are among the most challenging due to their huge dynamic ranges and the frequent presence of large noise-dominated regions in the images. We show that high-quality image reconstruction is possible even in super-resolution and without the use of traditional regularization terms. Using a robust \r{ho}-function is straightforward to implement in a streaming setting and, hence our method is applicable to the large volumes of astronomy images. The power of our method is demonstrated on observations from the Sloan Digital Sky Survey (Stripe 82) and we briefly discuss the feasibility of a pipeline based on Graphical Processing Units for the next generation of telescope surveys.