  Motivated by an application in high-throughput genomics and metabolomics, we
propose a novel, efficient and fully data-driven approach for estimating large
block structured sparse covariance matrices in the case where the number of
variables is much larger than the number of samples without limiting ourselves
to block diagonal matrices. Our approach consists in approximating such a
covariance matrix by the sum of a low-rank sparse matrix and a diagonal matrix.
Our methodology also can deal with matrices for which the block structure
appears only if the columns and rows are permuted according to an unknown
permutation. Our technique is implemented in the R package \texttt{BlockCov}
which is available from the Comprehensive R Archive Network (CRAN) and from
GitHub. In order to illustrate the statistical and numerical performance of our
package some numerical experiments are provided as well as a thorough
comparison with alternative methods. Finally, our approach is applied to the
use of "multi-omic" approaches for studying seed quality.
