Grégory Sainton

Ali Siahkoohi, Rudy Morel, Maarten V. de Hoop et al.

Source separation involves the ill-posed problem of retrieving a set of source signals that have been observed through a mixing operator. Solving this problem requires prior knowledge, which is commonly incorporated by imposing regularity conditions on the source signals, or implicitly learned through supervised or unsupervised methods from existing data. While data-driven methods have shown great promise in source separation, they often require large amounts of data, which rarely exists in planetary space missions. To address this challenge, we propose an unsupervised source separation scheme for domains with limited data access that involves solving an optimization problem in the wavelet scattering covariance representation space$\unicode{x2014}$an interpretable, low-dimensional representation of stationary processes. We present a real-data example in which we remove transient, thermally-induced microtilts$\unicode{x2014}$known as glitches$\unicode{x2014}$from data recorded by a seismometer during NASA's InSight mission on Mars. Thanks to the wavelet scattering covariances' ability to capture non-Gaussian properties of stochastic processes, we are able to separate glitches using only a few glitch-free data snippets.

Ali Siahkoohi, Rudy Morel, Randall Balestriero et al.

Unsupervised source separation involves unraveling an unknown set of source signals recorded through a mixing operator, with limited prior knowledge about the sources, and only access to a dataset of signal mixtures. This problem is inherently ill-posed and is further challenged by the variety of timescales exhibited by sources in time series data from planetary space missions. As such, a systematic multi-scale unsupervised approach is needed to identify and separate sources at different timescales. Existing methods typically rely on a preselected window size that determines their operating timescale, limiting their capacity to handle multi-scale sources. To address this issue, we propose an unsupervised multi-scale clustering and source separation framework by leveraging wavelet scattering spectra that provide a low-dimensional representation of stochastic processes, capable of distinguishing between different non-Gaussian stochastic processes. Nested within this representation space, we develop a factorial variational autoencoder that is trained to probabilistically cluster sources at different timescales. To perform source separation, we use samples from clusters at multiple timescales obtained via the factorial variational autoencoder as prior information and formulate an optimization problem in the wavelet scattering spectra representation space. When applied to the entire seismic dataset recorded during the NASA InSight mission on Mars, containing sources varying greatly in timescale, our approach disentangles such different sources, e.g., minute-long transient one-sided pulses (known as "glitches") and structured ambient noises resulting from atmospheric activities that typically last for tens of minutes, and provides an opportunity to conduct further investigations into the isolated sources.