Image deconvolution using incomplete Fourier measurements

In this article, we propose a new deconvolution algorithm, which is based on image reconstruction from incomplete measurements in Fourier domain. Our algorithm has two steps. First, an initial estimator is obtained using Fourier regularized inverse operator. Second, parts of the estimator's Fourier coefficients are saved, and the others are removed to suppress noise energy, then the remaining coefficients are used to recover image based on the sparse constraints. This image reconstruction problem is an optimization problem that is solved by a fast algorithm named split Bregman iteration. Different from other deconvolution algorithms, our algorithm only uses parts of Fourier components to restore the blurred image and combines two different regularization strategies efficiently by applying a selection matrix. The experiment shows that our method gives better performance than many other competitive deconvolution methods. © 2012 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 22, 233–240, 2012