Improvement of Space-Invariant Image Deblurring by Preconditioned Landweber Iterations

Abstract

The Landweber method is a simple and flexible iterative regularization algorithm,
\nwhose projected variant provides nonnegative image reconstructions. Since the method is usually very
\nslow, we apply circulant preconditioners, exploiting the shift invariance of many deblurring problems,
\nin order to accelerate the convergence. This way reasonable reconstructions can be obtained within
\na few iterations; the method becomes competitive and more robust than other approaches that,
\nalthough faster, sometimes lead to lower accuracy. Some theoretical analysis of convergence is given,
\ntogether with numerical validations.