Blind source separation over space: an eigenanalysis approach

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.