Kronecker covariance sketching for spatial-temporal data

Covariance sketching has been recently introduced as an effective strategy to reduce the data dimensionality without sacrificing the ability to reconstruct second-order statistics of the data. In this paper, we propose a novel covariance sketching scheme with reduced complexity for spatial-temporal data, whose covariance matrices satisfy the Kronecker product expansion model recently introduced by Tsiligkaridis and Hero. Our scheme is based on quadratic sampling that only requires magnitude measurements, hence is appealing for applications when phase information is difficult to obtain, such as wideband spectrum sensing and optical imaging. We propose to estimate the covariance matrix based on convex relaxation when the separation rank is small, and when the temporal covariance is additionally Toeplitz structured. Numerical examples are provided to demonstrate the effectiveness of the proposed scheme.