Simultaneous recovery of attenuation and source density in SPECT

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Inverse Problems and Imaging Pub Date : 2022-06-21 DOI:10.3934/ipi.2023005

S. Holman, Philip Richardson

引用次数: 0

Abstract

We show that under a certain non-cancellation condition the attenuated Radon transform uniquely determines piecewise constant attenuation $a$ and piecewise $C^2$ source density $f$ with jumps over real analytic boundaries possibly having corners. We also look at numerical examples in which the non-cancellation condition fails and show that unique reconstruction of multi-bang $a$ and $f$ is still appears to be possible although not yet explained by theoretical results.

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SPECT中衰减和源密度的同时恢复

我们证明了在一定的非相消条件下，衰减的Radon变换唯一地确定了分段常数衰减$a$和分段源密度$f$，并且跨越了可能具有角的实分析边界。我们还研究了非抵消条件失败的数值例子，并表明多重爆炸$a$和$f$的唯一重建似乎仍然是可能的，尽管理论结果尚未解释。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Inverse Problems and Imaging 数学-物理：数学物理

CiteScore

2.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Inverse Problems and Imaging publishes research articles of the highest quality that employ innovative mathematical and modeling techniques to study inverse and imaging problems arising in engineering and other sciences. Every published paper has a strong mathematical orientation employing methods from such areas as control theory, discrete mathematics, differential geometry, harmonic analysis, functional analysis, integral geometry, mathematical physics, numerical analysis, optimization, partial differential equations, and stochastic and statistical methods. The field of applications includes medical and other imaging, nondestructive testing, geophysical prospection and remote sensing as well as image analysis and image processing. This journal is committed to recording important new results in its field and will maintain the highest standards of innovation and quality. To be published in this journal, a paper must be correct, novel, nontrivial and of interest to a substantial number of researchers and readers.