A Data-Driven Iteratively Regularized Landweber Iteration
A. Aspri, S. Banert, O. Öktem, O. Scherzer
Abstract
We derive and analyze a new variant of the iteratively regularized Landweber iteration, for solving linear and nonlinear ill-posed inverse problems. The method takes into account training data, which are used to estimate the interior of a black box, which is used to define the iteration process. We prove convergence and stability for the scheme in infinite dimensional Hilbert spaces. These theoretical results are complemented by some numerical experiments for solving linear inverse problems for the Radon transform and a nonlinear inverse problem for Schlieren tomography.
Topics & Concepts
MathematicsInverse problemConvergence (economics)InverseApplied mathematicsNonlinear systemStability (learning theory)Iterative methodHilbert spaceRadon transformMathematical analysisInterpolation (computer graphics)Scheme (mathematics)Regularization (linguistics)Linear systemNumerical stabilityHilbert transformNumerical analysisPoint (geometry)Linear mapGeneralized inverseNumerical methods in inverse problemsMicrowave Imaging and Scattering AnalysisSparse and Compressive Sensing Techniques