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\begin{enumerate}  \item The dictionary $\mathbf{A} \in \mathbb{R}^{n \times n}$ is a 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}  The main result is that when $\theta \in (0, 1/3)$, $\mathbf{A}_0$ and $\mathbf{X}_0$ can be exactly recovered with a polynomial time algorithm with high probability, if number of samples $p$ is no less than a polynomial of $(n, 1/\theta, \kappa(\mathbf{A}_0), 1/\mu)$, where $\kappa(\mathbf{A}_0)$ is the conditional number of the dictionary.  \end{enumerate}