Restoration of blurred star field images by maximally sparse optimization

In this paper we address the problem of removing blur from, or sharpening, astronomical star field intensity images. A new approach to image restoration 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). is presented and candidate algorithms for solving the ensuing nonlinear constrained optimization problem are presented and reviewed. Synthetic and actual star image reconstruction examples are presented which demonstrate the method's superior performance as compared with several standard image deconvolution methods.