We address the problem of resolving blurred point sources in intensity images. A new approach to image restoration is introduced which is a 2-D generalization of techniques originating from the field of direction of arrival estimation (DOA). In the 2-D frequency domain, algorithms, such as MUSIC, may be adapted to search for these point sources. A generalization of array smoothing based on a regularization operator is introduced for 2-D arrays in order to achieve rank enhancement in the signal space of the covariance matrix.>

This paper addresses the problem of resolving and localizing blurred point sources in intensity images, such as atmospherically blurred star images. It is shown that this problem can be modeled in a form similar to that used for sensor array data in direction of arrival (DOA) estimation. A new superresolving restoration algorithm is described as a generalization of eigenstructure decomposition methods popular in DOA estimation. The algorithm includes a signal subspace rank enhancement technique that works in the presence of non-uniform element weighting due to blur. A theoretical analysis of source localization error is presented, and an expression predicting error performance is derived. Restoration examples are presented illustrating the accuracy of the error analysis and demonstrating algorithm performance.>

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.