Fig. 1: Workflow of our unsupervied imaging method.
From: Inverse imaging with elastic waves driven by unsupervised machine learning
a Setup for obtaining vibration fields by a laser Doppler vibrometer for the inverse imaging of parameters \(\left\{{\alpha }_{i}\right\}=\{{E}_{0},{h}_{1},{h}_{2},{h}_{3}\}\), i.e., Young’s modulus and three heights of a beam, which is excited by a harmonic signal at one end at \(f=2{{\rm{kHz}}}\). b, c The architecture of the machine learning model, with b a variational autoencoder (VAE-Net, filled with gray color) to compress the velocity fields \(\{{v}_{i}\}\) into a low-dimensional representation \(\left\{{z}_{i}\right\}\) (each follows a Gaussian distribution with mean \({\mu }_{i}\) and standard deviation \({\sigma }_{i}\) in generating the latent variable for every input), and c an independent component analysis (ICA-Net, filled with light blue color) to further transform \(\{{z}_{i}\}\) into their independent components \(\{{z}_{i}^{{\prime} }\}\). The predicted values \(\left\{{\alpha }_{i}^{{\prime} }\right\}=\{{E}_{0}^{{\prime} },{h}_{1}^{{\prime} },{h}_{2}^{{\prime} },{h}_{3}^{{\prime} }\}\) can be readily obtained by linearly scaling \(\{{z}_{i}^{{\prime} }\}\) with a small amount of \(\left\{{z}_{i}^{{\prime} },{\alpha }_{i}\right\}\) pairs to correct the range of each \({z}_{i}^{{\prime} }\), as shown in (d) (filled with light green color).
