Abel inversion using total variation regularization: applications

被引：19

作者：

Asaki, Thomas J. ^{[1
]}

Campbell, Patrick R. ^{[1
]}

Chartrand, Rick ^{[1
]}

Powell, Collin E. ^{[1
]}

Vixie, Kevin R. ^{[1
]}

Wohlberg, Brendt E. ^{[1
]}

机构：

[1] Los Alamos Natl Lab, Los Alamos, NM 87545 USA

来源：

INVERSE PROBLEMS IN SCIENCE AND ENGINEERING | 2006年 / 14卷 / 08期

关键词：

Abel transform; inverse problems; total variation; tomography; regularization;

D O I：

10.1080/17415970600882549

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

We apply total-variation (TV) regularization methods to Abel inversion tomography. inversions are performed using the fixed-point iteration method and the regularization parameter is chosen such that the resulting data fidelity approximates the known or estimated statistical character of the noisy data. Five one-dimensional (ID) examples illustrate the favorable characteristics of TV-regularized solutions: noise suppression and density discontinuity preservation. Experimental and simulated examples from X-ray radiography also illustrate limitations due to a linear projection approximation. TV-regularized inversions are shown to be superior to squared gradient (Tikhonov) regularized inversions for objects with density discontinuities. We also introduce an adaptive TV method that utilizes a modified discrete gradient operator acting only apart from data-determined density discontinuities. This method provides improved density level preservation relative to the basic TV method.

引用

页码：873 / 885

页数：13

共 4 条

[1]

[Anonymous], 1987, FRONT APPL MATH, DOI DOI 10.1137/1.9780898717570

[2] Abel inversion using total-variation regularization [J].