Tomographic imaging of non-local media based on space-fractional diffusion models
Tomographic imaging of non-local media based on space-fractional diffusion models
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DOI：
10.1063/1.5026789
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发表时间：
2018-06
影响因子：
3.2
通讯作者：
Salvatore Buonocore;F. Semperlotti
中科院分区：
文献类型：
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作者：
Salvatore Buonocore;F. Semperlotti
我们研究了一种适用于一类非局部扩散能量输运的非均匀介质的广义层析成像框架。在这些条件下，通过分数阶连续体模型可以很好地描述输运机制，该模型能够捕获异常扩散，否则使用传统的整数阶模型将无法检测到异常扩散。虽然所提出的框架的基本思想适用于任何传输机制，但分数热传导的情况是作为一个具体的例子来说明该方法。通过数值模拟，我们展示了如果使用分数阶模型，涉及非局部输运的复杂非均匀介质是如何成功成像的。特别是，结果将表明，通过正确识别和考虑宿主介质的分数特征，不仅可以实现更高的分辨率，而且在强和空间分布的非局域性的情况下，它代表了实现成功重建的唯一可行方法。我们研究了一种适用于一类非局部扩散能量输运的非均匀介质的广义层析成像框架。在这些条件下，通过分数阶连续体模型可以很好地描述输运机制，该模型能够捕获异常扩散，否则使用传统的整数阶模型将无法检测到异常扩散。虽然所提出的框架的基本思想适用于任何传输机制，但分数热传导的情况是作为一个具体的例子来说明该方法。通过数值模拟，我们展示了如果使用分数阶模型，涉及非局部输运的复杂非均匀介质是如何成功成像的。特别是，结果将表明，通过正确识别和考虑宿主介质的分数特征，不仅可以实现更高的分辨率，而且在强和空间分布的非局部性的情况下，它代表了唯一可行的…
We investigate a generalized tomographic imaging framework applicable to a class of inhomogeneous media characterized by non-local diffusive energy transport. Under these conditions, the transport mechanism is well described by fractional-order continuum models capable of capturing anomalous diffusion that would otherwise remain undetected when using traditional integer-order models. Although the underlying idea of the proposed framework is applicable to any transport mechanism, the case of fractional heat conduction is presented as a specific example to illustrate the methodology. By using numerical simulations, we show how complex inhomogeneous media involving non-local transport can be successfully imaged if fractional order models are used. In particular, results will show that by properly recognizing and accounting for the fractional character of the host medium not only allows achieving increased resolution but, in case of strong and spatially distributed non-locality, it represents the only viable approach to achieve a successful reconstruction.We investigate a generalized tomographic imaging framework applicable to a class of inhomogeneous media characterized by non-local diffusive energy transport. Under these conditions, the transport mechanism is well described by fractional-order continuum models capable of capturing anomalous diffusion that would otherwise remain undetected when using traditional integer-order models. Although the underlying idea of the proposed framework is applicable to any transport mechanism, the case of fractional heat conduction is presented as a specific example to illustrate the methodology. By using numerical simulations, we show how complex inhomogeneous media involving non-local transport can be successfully imaged if fractional order models are used. In particular, results will show that by properly recognizing and accounting for the fractional character of the host medium not only allows achieving increased resolution but, in case of strong and spatially distributed non-locality, it represents the only viable ...