Restoration of blurred star field images by maximally sparse optimization

The problem of removing blur from, or sharpening, astronomical star field intensity images is discussed. An approach to image restoration that recovers image detail using a constrained optimization theoretic approach is introduced. Ideal star images may be modeled as a few point sources in a uniform background. It is 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 to demonstrate the method's superior performance as compared with several image deconvolution methods.