Blind Source Separation over Space

TL;DR

This paper introduces a novel eigenanalysis-based method for blind source separation in spatial data, capable of handling high-dimensional fields with proven consistency and error bounds, demonstrated through simulations and real data.

Contribution

It presents a new estimation technique using eigenanalysis of spatial covariance matrices, improving robustness and applicability in high-dimensional spatial blind source separation.

Findings

Method is consistent with explicit error rates.

Effective in moderately high-dimensional settings.

Validated through simulations and real-world data.

Abstract

We propose a new estimation method for the blind source separation model of Bachoc et al. (2020). The new estimation is based on an eigenanalysis of a positive definite matrix defined in terms of multiple normalized spatial local covariance matrices, and, therefore, can handle moderately high-dimensional random fields. The consistency of the estimated mixing matrix is established with explicit error rates even when the eigen-gap decays to zero slowly. The proposed method is illustrated via both simulation and a real data example.