I. Introduction
Suppose we are given a data matrix that was obtained from the following model \begin{equation*} Y= \frac{1}{\sqrt{N}}X^{T}X+W, \tag{1} \end{equation*}
where is a matrix in . Each of the elements of is an independent random variable in Rr distributed according to . Further is a symmetric noise matrix with elements distributed as . The observation thus consists of a rank matrix corrupted by a Gaussian noise. The main difficulty, but also interest, stems from the fact that we require to be sparse: only a fraction of elements of are non-zero and is constrained accordingly.