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The data matrix is generated as $\mathbf{Y} = \mathbf{A}_0 \mathbf{X}_0$, where $\mathbf{Y} \in \mathbb{R}^{n \times p}$, and the following conditions are assumed.   \begin{enumerate}  \item The dictionary $\mathbf{A} \in \mathbb{R}^{n \times n}$ is a complete, namely  square and invertible. \item The elements in $\mathbf{X}_0$ is independently drawn from Bernoulli-Gaussian (BG) model. $X_{0{[ij]}} = \Omega_{ij} V_{ij}$, where $\Omega_{ij} \sim \text{Ber}(\theta)$ and $V_{ij} \sim N(0,1)$.   \end{enumerate}