Image deblurring based on ForIcM: Fourier shrinkage and incomplete measurements

Abstract

In this paper, we propose a new deblurring algorithm, which is based on image reconstruction from incomplete measurements in Fourier domain. Our algorithm has two steps. Firstly, an initial estimator is obtained using Fourier regularised inverse operator. Secondly, parts of the estimator’s Fourier coefficients are saved, and the others are removed to suppress noise energy, and then the remaining coefficients are used to recover image based on the sparse constraints. This image reconstruction problem is an optimisation problem which is solved by a fast algorithm named split Bregman iteration. Our algorithm combines two different regularisation strategies efficiently by applying a selection matrix. The tests using images with different blurs and noise produce good results. The experiment shows that our method gives better performance than many other competitive deblurring methods.

Keywords:

• image deconvolution
• image deblurring
• restoration
• split Bregman iteration
• incomplete measurements