Solving or resolving inadequate and noisy tomographic systems
type: Item
instance of: scholarly article
title: Solving or resolving inadequate and noisy tomographic systems
zbMATH Open document ID: 0589.65086
DOI: 10.1016/0021-9991(85)90075-0
author: Guust Nolet
published in: Journal of Computational Physics
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://dspace.library.uu.nl/handle/1874/16491
review text: The determination of seismic velocity leads to the inversion of the Radon transform; i.e., line integrals of the searched-for distribution are given. In contrast to medicals application the data cannot be collected uniformly, resulting in a highly ill-posed problem. Also the recovery is complicated by very noisy data. The projection of the solution onto a finite dimensional pixel space then leads to very ill-conditioned linear equations. The author compares different stabilization methods, namely singular value decomposition (SVD), conjugate gradients (CG) and the Dines-Lytle method, which is a version of the Landweber iteration. It turns out that the CG-method is cheaper than SVD and that it picks up the recoverable part of the solution after a few steps. The Dines-Lytle method is much slower. In a resolution analysis the trade-off between resolution and noise damping is studied.
Mathematics Subject Classification ID: 65R10
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 86A15
Mathematics Subject Classification ID: 44A15
zbMATH DE Number: 3947576
zbMATH Keywords: tomography
zbMATH Keywords: regularisation by iterative methods
zbMATH Keywords: seismology
zbMATH Keywords: inversion
zbMATH Keywords: Radon transform
zbMATH Keywords: ill-posed problem
zbMATH Keywords: noisy data
zbMATH Keywords: stabilization methods
zbMATH Keywords: singular value decomposition
zbMATH Keywords: conjugate gradients
zbMATH Keywords: Dines-Lytle method
zbMATH Keywords: Landweber iteration
describes a project that uses: LSQR
MaRDI profile type: Publication
OpenAlex ID: W2086784326
cites work: Accelerated projection methods for computing pseudoinverse solutions of systems of linear equations
cites work: Calculating the Singular Values and Pseudo-Inverse of a Matrix
cites work: LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
cites work: Q3968572
description: scientific article; zbMATH DE number 3947576