The Approximate Inverse in Action with an Application to Computerized Tomography

DOI10.1137/S0036142998347619zbMath0961.65112MaRDI QIDQ4509662

Andreas Rieder, Thomas Schuster

Publication date: 19 October 2000

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

zbMATH Keywords

algorithmRadon transformsingular value decompositionerror analysiscomputerized tomographynumerical inversionlinear operator equationsreconstructionapproximate inversemollificationfiltered backprojection

Mathematics Subject Classification ID

Biomedical imaging and signal processing (92C55) Radon transform (44A12) Numerical methods for integral transforms (65R10) Numerical solutions to equations with linear operators (65J10) Equations and inequalities involving linear operators, with vector unknowns (47A50) Numerical methods for ill-posed problems for integral equations (65R30) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Linear operators and ill-posed problems, regularization (47A52)

Related Items (14)

The approximate inverse in action II: convergence and stability ⋮ Error estimates and convergence rates for filtered back projection ⋮ Linear Functional Strategy and the Approximate Inverse for Nonlinear Ill-Posed Problems ⋮ A Galerkin Least Squares Approach for Photoacoustic Tomography ⋮ Approximate inverse method for stable analytic continuation in a strip domain ⋮ The method of approximate inverse for the Radon transform operator acting on functions and for the normal Radon transform operators acting on vector and symmetric 2-tensor fields in \(\mathbb R^3\) ⋮ The Method of Approximate Inverse in Slice-by-Slice Vector Tomography Problems ⋮ Inverse problems with inexact forward operator: iterative regularization and application in dynamic imaging ⋮ Error analysis for filtered back projection reconstructions in Besov spaces ⋮ Optimality of the fully discrete filtered backprojection algorithm for tomographic inversion ⋮ Numerical rate function determination in partial differential equations modeling cell population dynamics ⋮ Finite dimensional realization of mollifier method: A new stable approach ⋮ A finite dimensional realization of the mollifier method for compact operator equations ⋮ The Method of Approximate Inverse for Ray Transform Operators on Two-Dimensional Symmetric m-Tensor Fields

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