Imaging by Unsupervised Feature Learning of the Wave Equation

We approach the inverse problem of imaging as a task of automated feature learning of the underlying wave equation. While feature extraction with unsupervised machine learning is widely used in analyzing complex data on clustering, classification, and visualization, we show its direct usage on discovering interpretable physical concepts and then obtaining images from wave-propagation data. By using a spring-mass lattice as a simplified model in acoustic imaging, a variational autoencoder is trained to extract features that govern the dynamics of wave propagation from configurations with uncorrelated random material parameters. The extracted features are transformed to images of spring constants and masses by an additional linear regression. The current scheme of extraction-based inverse imaging of features is robust against noise in wave-propagation data and incomplete accessibility in the case of inverse scattering in practice. Our approach requires minimal prior knowledge of the wave-scattering mechanism with applications from the extraction of physical constants and defect detection to discovering physical phenomena.