  Matrix completion problem has been previously studied under various adaptive
and passive settings. Previously, researchers have proposed passive, two-phase
and single-phase algorithms using coherence parameter, and multi phase
algorithm using sparsity-number. It has been shown that the method using
sparsity-number reaching to theoretical lower bounds in many conditions.
However, the aforementioned method is running in many phases through the matrix
completion process, therefore it makes much more informative decision at each
stage. Hence, it is natural that the method outperforms previous algorithms. In
this paper, we are using the idea of sparsity-number and propose and
single-phase column space recovery algorithm which can be extended to two-phase
exact matrix completion algorithm. Moreover, we show that these methods are as
efficient as multi-phase matrix recovery algorithm. We provide experimental
evidence to illustrate the performance of our algorithm.
