Martian time-series unraveled: A multi-scale nested approach with factorial variational autoencoders

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 time-scales exhibited by sources in time series data from planetary space missions. As such, a systematic multiscale unsupervised approach is needed to identify and separate sources at different time-scales. Existing methods typically rely on a preselected window size that determines their operating time-scale, limiting their capacity to handle multi-scale sources. To address this issue, instead of directly operating in the time domain, we propose an unsupervised multi-scale clustering and source separation framework by leveraging wavelet scattering covariances that provide a low-dimensional representation of stochastic processes, capable of effectively distinguishing between different non-Gaussian stochastic processes. Nested within this representation space, we develop a factorial Gaussian-mixture variational autoencoder that is trained to (1) probabilistically cluster sources at different time-scales and (2) independently sample scattering covariance representations associated with each cluster. As the final stage, using samples from each cluster as prior information, we formulate source separation as an optimization problem in the wavelet scattering covariance representation space, resulting in separated sources in the time domain. When applied to seismic data recorded during the NASA InSight mission on Mars, containing sources varying greatly in time-scale, our multi-scale nested approach proves to be a powerful tool for discriminating between 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. These results provide an opportunity to conduct further investigations into the isolated sources related to atmospheric-surface interactions, thermal relaxations, and other complex phenomena.