A popular approach to recover low rank matrices is the nuclear norm regularized minimization (NRM) for which the selection of the regularization parameter is inevitable. In this paper, we build up a novel rule to choose the regularization parameter for NRM, with the help of the duality theory. Our result provides a safe set for the regularization parameter when the rank of the solution has an upper bound. Furthermore, we apply this idea to NRM with quadratic and Huber functions, and establish simple formulae for the regularization parameters. Finally, we report numerical results on some signal shapes by embedding our rule into the cross validation, which state that our rule can reduce the computational time for the selection of the regularization parameter. To the best of our knowledge, this is the first attempt to select the regularization parameter for the low rank matrix recovery.

恢复低秩矩阵的一种流行方法是核规范正则化最小化（NRM），对于该规范，选择正则化参数是不可避免的。在本文中，我们借助对偶理论，建立了一种新的规则来选择NRM的正则化参数。当解决方案的等级有上限时，我们的结果为正则化参数提供了一个安全的设置。此外，我们将此思想应用于具有二次函数和Huber函数的NRM，并为正则化参数建立了简单的公式。最后，我们通过将规则嵌入交叉验证来报告某些信号形状的数值结果，这表明我们的规则可以减少选择正则化参数的计算时间。据我们所知，