  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.
