Landweber iteration

Landweber iteration is a regularizing algorithm used in numerical analysis to solve inverse problems. It is a method of updating an initial estimate of a solution by iteratively applying a linear operator and subtracting the difference between the result and the observed data. As the number of iterations tends to infinity, the iterate approaches the generalised inverse. The update equation obtained by using the MM procedure is known as the Landweber iteration.From: The Limits of Resolution [2019], Regularized Image Reconstruction in Parallel MRI with MATLAB® [2019]

Regularization Techniques for MR Image Reconstruction

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Published in Joseph Suresh Paul, Raji Susan Mathew, Regularized Image Reconstruction in Parallel MRI with MATLAB®, 2019

Joseph Suresh Paul, Raji Susan Mathew

This update equation obtained by using the MM procedure is known as the Landweber iteration. The Landweber iteration can be used only if the objective function contains differentiable convex functions. However, if the objective function contains terms for which differentiation cannot be obtained directly, then a proximal operator becomes necessary to obtain the solution.

On the second-order asymptotical regularization of linear ill-posed inverse problems

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Published in Applicable Analysis, 2020

Y. Zhang, B. Hofmann

From a computational viewpoint, the Landweber iteration, as well as the steepest descent method and the minimal error method, is quite slow. Therefore, in practice accelerating strategies are usually used; see [3,7] and references therein for details.

Landweber iteration

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Regularization Techniques for MR Image Reconstruction

On the second-order asymptotical regularization of linear ill-posed inverse problems