Accelerated Landweber iteration with convex penalty for linear inverse problems in Banach spaces

DOI10.1080/00036811.2014.912751zbMath1311.65054OpenAlexW2024569854WikidataQ58274384 ScholiaQ58274384MaRDI QIDQ4982029

Markus Hegland, Wei Wang, Qi-nian Jin

Publication date: 23 March 2015

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036811.2014.912751

zbMATH Keywords

numerical examplesaccelerationLandweber iterationlinear inverse problemssubspace optimizationnonsmooth regularization

Mathematics Subject Classification ID

Numerical solutions to equations with linear operators (65J10) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Linear operators and ill-posed problems, regularization (47A52) Numerical solution to inverse problems in abstract spaces (65J22)

Related Items (13)

REGINN-IT method with general convex penalty terms for nonlinear inverse problems ⋮ A novel two-point gradient method for regularization of inverse problems in Banach spaces ⋮ Generalized inexact Newton regularization for nonlinear ill-posed problems in Banach spaces ⋮ A fast two-point gradient algorithm based on sequential subspace optimization method for nonlinear ill-posed problems ⋮ A Fast Data-Driven Iteratively Regularized Method with Convex Penalty for Solving Ill-Posed Problems ⋮ An accelerated Kaczmarz type method for nonlinear inverse problems in Banach spaces with uniformly convex penalty ⋮ Inexact Newton regularization in Banach spaces based on two-point gradient method with uniformly convex penalty terms ⋮ An accelerated sequential subspace optimization method based on homotopy perturbation iteration for nonlinear ill-posed problems ⋮ An accelerated homotopy perturbation iteration for nonlinear ill-posed problems in Banach spaces with uniformly convex penalty ⋮ Fast subspace optimization method for nonlinear inverse problems in Banach spaces with uniformly convex penalty terms ⋮ Accelerated homotopy perturbation iteration method for a non-smooth nonlinear ill-posed problem ⋮ Regularization of inverse problems by two-point gradient methods in Banach spaces ⋮ Inexact Newton regularization combined with two-point gradient methods for nonlinear ill-posed problems ^*

Cites Work

• Nonlinear total variation based noise removal algorithms
• A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
• Nonsmooth analysis
• Accelerated Landweber iterations for the solution of ill-posed equations
• Landweber iteration of Kaczmarz type with general non-smooth convex penalty functionals
• Iterative regularization with a general penalty term—theory and application to L ¹ and TV regularization
• Fast regularizing sequential subspace optimization in Banach spaces
• Regularizing properties of a truncated newton-cg algorithm for nonlinear inverse problems
• Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems

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