A Mathematical Framework for Deep Learning in Elastic Source Imaging

Jaejun Yoo; Abdul Wahab; Jong Chul Ye

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arXiv · 1802.10055

A Mathematical Framework for Deep Learning in Elastic Source Imaging

Jaejun Yoo·Abdul Wahab·Jong Chul Ye

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Abstract

An inverse elastic source problem with sparse measurements is of concern. A generic mathematical framework is proposed which incorporates a low- dimensional manifold regularization in the conventional source reconstruction algorithms thereby enhancing their performance with sparse datasets. It is rigorously established that the proposed framework is equivalent to the so-called \emph{deep convolutional framelet expansion} in machine learning literature for inverse problems. Apposite numerical examples are furnished to substantiate the efficacy of the proposed framework.

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Jaejun Yoo, Abdul Wahab, Jong Chul Ye. 2018-02-27. A Mathematical Framework for Deep Learning in Elastic Source Imaging. https://arxiv.org/abs/1802.10055

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