A Learned-SVD approach for Regularization in Diffuse Optical Tomography

Abstract

Inverse problems arising in Diffuse Optical Tomography are severely ill-conditioned • Traditional approaches rely on regularization functions with fine tuning of parameters • We explore deep learning techniques in a fully data-driven approach • The approach is the deep learning equivalent of the SVD of a nonlinear functional • The solution is robust even in presence of high levels of noise

An autoencoder solution for the electromagnetic inverse source problem

“…The DL technique here considered, known as Learned SVD (L-SVD), is a fully data-driven strategy that combines three neural networks (NNs): a data autoencoder, a source autoencoder, and a scaling layer connecting the latent spaces associated with the data and the source. This approach has been introduced in [13] and later applied to diffuse optical tomography [14]. Through numerical simulations, we demonstrate that, in the benchmark case of noiseless data, the L-SVD inversion strategy surpasses the TSVD scheme by providing lower reconstruction errors so enabling the recovery of faster spatial variations of the radiating source.…”