<p>The problem of image deblurring consists in restoring a clean image from a given blurry image, typically corrupted by noise. In this work, we propose accelerated schemes inspired by variants of the Landweber iterations. The main idea consists of interpreting these iterations as gradient descent steps, using an appropriate conditioning of the gradient directions by a correction term, and accelerating the iterations by using alternating step sizes. Numerical experiments show that the combination of these different ingredients leads to improvements in image deblurring tasks. In particular, we show that the results obtained improve over state-of-the-art methods. We also show that the proposed approach can be adapted and used for more general black-box defiltering tasks, and, in particular, show its performance for the problem of enhancing low-light and blurry images in the presence of noise.</p>