An autoencoder-based model for learning regularizations in unmixing problems

Signal unmixing is a class of complex, ill-posed inverse problems, which includes blind source separation or underdetermined signal separation to cite only two. Retrieving signals from their mixtures generally relies on adapted representations allowing to disentangle them. When dealing with real-world scientific data, the main challenge is to further build meaningful signal representations, which generally means capturing the underlying low-dimensional manifold structure of the signals to be recovered. Since the latter is generally unknown, this calls for a learning-based approach, which is a challenging task, especially when available training samples are scarce. The objective of the paper is to investigate a new learning model to build low-dimensional signal representations from few training samples. Based on an encoder-decoder architecture, the proposed approach aims to learn a non-linear interpolating scheme from examples. Extensive numerical experiments have been carried out to evaluate the performances of the proposed approach. We further illustrate how the learned representations can be conveniently deployed to tackle challenging semi-blind unmixing problems in the field of γ-ray spectroscopy.