An optimal condition of robust low-rank matrices recovery

Jianwen Huang, Sanfu Wang, Jianjun Wang, Feng Zhang, Hailin Wang, Jinping Jia

Abstract

In this paper we investigate the reconstruction conditions of nuclear norm minimization for low-rank matrix recovery.We obtain sufficient conditions δtr < t/(4 -t) with 0 < t < 4/3 to guarantee the robust reconstruction (z = 0) or exact reconstruction (z = 0) of all rank r matrices X ∈ R m×n from b = A(X)+z via nuclear norm minimization.Furthermore, we not only show that when t = 1, the upper bound of δr < 1/3 is the same as the result of Cai and Zhang [14], but also demonstrate that the gained upper bounds concerning the recovery error are better.Moreover, we prove that the restricted isometry property condition is sharp.Besides, the numerical experiments are conducted to reveal the nuclear norm minimization method is stable and robust for the recovery of low-rank matrix.

Locations

• International Journal of Wireless and Mobile Computing - View
• arXiv (Cornell University) - View - PDF