Abstract: In this paper we address the problem of removing blur from, or sharpening, astronomical star field intensity images. A new image restoration algorithm is introduced which recovers image detail using a constrained optimization theoretic approach. Ideal star images may be modeled as a few point sources in a uniform background. It is therefore argued that a direct measure of image sparseness is the appropriate optimization criterion for deconvolving the image blurring function. A sparseness criterion based on the l$-p$/ quasinorm is presented and algorithms for sparse reconstruction are described. Synthetic and actual star image reconstruction examples are presented which demonstrate the algorithm's superior performance as compared with the CLEAN algorithm, a standard star field deconvolution method. !13
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