Estimation of the sample covariance matrix from compressive measurements

TL;DR

This paper introduces an unbiased method for estimating the sample covariance matrix from compressive measurements using general random projections, applicable without structural assumptions and suitable for resource-limited devices.

Contribution

We propose a novel unbiased estimator for covariance from compressive measurements that does not assume low-rank structure and works with sparse Rademacher matrices.

Findings

Accurate covariance estimation demonstrated on real-world datasets

Method works without structural assumptions on covariance

Effective with sparse projection matrices

Abstract

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.