An Algebraic Method for Reconstruction of Harmonic Functions via Radon Projections

被引：1

作者：

Georgieva, I. ^{[1
]}

Hofreither, C. ^{[2
]}

机构：

[1] Bulgarian Acad Sci, Inst Math & Informat, Acad G Bontchev Str,Bl 8, BU-1113 Sofia, Bulgaria

[2] Johannes Kepler Univ Linz, DK comp Math, A-4040 Linz, Austria

来源：

APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES | 2012年 / 1487卷

基金：

奥地利科学基金会;

关键词：

Computer tomography; Radon projections; Radon transform; FFT; image reconstrustion; harmonic interpolation; harmonic polynomials; noisy data; MULTIVARIATE INTERPOLATION; BIVARIATE POLYNOMIALS; GAUSSIAN QUADRATURE; LAGRANGE;

D O I：

10.1063/1.4758948

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider an algebraic method for reconstruction of a harmonic function via a finite number of values of its Radon projections. More precisely, for given values of some Radon projections, we seek a harmonic polynomial which matches these data exactly. In the present work, we focus mostly on the case where these measurements are taken along equally spaced chords of the unit circle. We present an efficient reconstruction algorithm which is robust with respect to noise in the input data and provide numerical examples.

引用

页码：112 / 119

页数：8

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