I have a matrix $X \in \mathbb{R}^{m\times n}$ and I want to estimate it with a dense matrix $Y^{m\times n}$ such that $Y$ is still close to $X$ in some distance measure. Is this doable in a computationally efficient way? While the sparse estimation is commonly used, but all my efforts for a regularization based solution ended up in nonconvex optimization.
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