Adaptive Landweber method to deblur images

Abstract

We present an adaptive Landweber method (ALM) to reconstruct an image from a blurred observation. The standard Landweber method (LM) is an iterative method to solve "ill-posed" problems encountered in image restoration. The standard LM uses a constant update parameter. It has the disadvantage of slow convergence. Instead of using a constant update parameter, the adaptive method computes the update parameter at each iteration. In the ALM, the adaptive update parameter is calculated as the ratio of the L/sub 2/ norm of the first-order derivatives of the restored images at current and previous iterations. The adaptive LM emphasizes speed at the beginning stages and stability at late stages of iteration. The ALM has a higher convergence rate and lower MSE and mean absolute error than the standard LM. We use examples to demonstrate the performance of the ALM.