Simultaneous recovery of attenuation and source density in SPECT

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research 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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.