A Mathematical Framework for Deep Learning in Elastic Source Imaging
This work addresses a domain-specific problem in elastic source imaging, likely for researchers in computational imaging or inverse problems, and appears incremental as it builds on existing reconstruction algorithms by adding regularization.
The authors tackled the inverse elastic source problem with sparse measurements by proposing a mathematical framework that incorporates low-dimensional manifold regularization into conventional reconstruction algorithms, which they rigorously established as equivalent to deep convolutional framelet expansion in machine learning, and they provided numerical examples to substantiate its efficacy.
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.