A novel gradient projection approach for Fourier-based image restoration

This work deals with the ill-posed inverse problem of reconstructing a two-dimensional image of an unknownobject starting from sparse and nonuniform measurements of its Fourier Transform. In particular, if we consider a prioriinformation about the target image (e.g., the nonnegativity of the pixels), this inverse problem can be reformulated as aconstrained optimization problem, in which the stationary points of the objective function can be viewed as the solutionsof a deconvolution problem with a suitable kernel. We propose a fast and effective gradient-projection iterative algorithmto provide regularized solutions of such a deconvolution problem by early stopping the iterations. Preliminary results on areal-world application in astronomy are presented.