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In this paper, we present a novel regularization with a truncated difference of nuclear norm and Frobenius norm of form   \begin{document}$ L_{t,*-\alpha F} $\end{document}   with an integer   \begin{document}$ t $\end{document}   and parameter   \begin{document}$ \alpha $\end{document}   for rank minimization problem. The forward-backward splitting (FBS) algorithm is proposed to solve such a regularization problem, whose subproblems are shown to have closed-form solutions. We show that any accumulation point of the sequence generated by the FBS algorithm is a first-order stationary point. In the end, the numerical results demonstrate that the proposed FBS algorithm outperforms the existing methods.

Low rank matrix minimization with a truncated difference of nuclear norm and Frobenius norm regularization