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An inverse elastic source problem with sparse measurements is of concern. Ageneric mathematical framework is proposed which incorporates a low-dimensional manifold regularization in the conventional source reconstructionalgorithms thereby enhancing their performance with sparse datasets. It isrigorously established that the proposed framework is equivalent to theso-called \emph{deep convolutional framelet expansion} in machine learningliterature for inverse problems. Apposite numerical examples are furnished tosubstantiate the efficacy of the proposed framework.

A Mathematical Framework for Deep Learning in Elastic Source Imaging