Adaptive Landweber method to deblur images

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 firstorder 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.