Estimation of the sample covariance matrix from compressive measurements
This work addresses covariance estimation for applications with limited memory and computation, such as acquisition devices, but is incremental as it builds on existing compressive sensing methods.
The paper tackles the problem of estimating the sample covariance matrix from low-dimensional compressive measurements without structural or distributional assumptions, presenting an unbiased estimator that achieves accurate results on real-world datasets like video data.
This paper focuses on the estimation of the sample covariance matrix from low-dimensional random projections of data known as compressive measurements. In particular, we present an unbiased estimator to extract the covariance structure from compressive measurements obtained by a general class of random projection matrices consisting of i.i.d. zero-mean entries and finite first four moments. In contrast to previous works, we make no structural assumptions about the underlying covariance matrix such as being low-rank. In fact, our analysis is based on a non-Bayesian data setting which requires no distributional assumptions on the set of data samples. Furthermore, inspired by the generality of the projection matrices, we propose an approach to covariance estimation that utilizes sparse Rademacher matrices. Therefore, our algorithm can be used to estimate the covariance matrix in applications with limited memory and computation power at the acquisition devices. Experimental results demonstrate that our approach allows for accurate estimation of the sample covariance matrix on several real-world data sets, including video data.