  Low rank matrix recovery is the focus of many applications, but it is a
NP-hard problem. A popular way to deal with this problem is to solve its convex
relaxation, the nuclear norm regularized minimization problem (NRM), which
includes LASSO as a special case. There are some regularization parameter
selection results for LASSO in vector case, such as screening rules, which
improve the efficiency of the algorithms. However, there are no corresponding
parameter selection results for NRM in matrix case. In this paper, we build up
a novel rule to choose the regularization parameter for NRM under the help of
duality theory. This rule claims that the regularization parameter can be
easily chosen by feasible points of NRM and its dual problem, when the rank of
the desired solution is no more than a given constant. In particular, we apply
this idea to NRM with least square and Huber functions, and establish the
easily calculated formula of regularization parameters. Finally, we report
numerical results on some signal shapes, which state that our proposed rule
shrinks the interval of the regularization parameter efficiently.
