The perturbation analysis of nonconvex low-rank matrix robust recovery
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In this paper, we bring forward a completely perturbed nonconvex Schatten p-minimization to address a model of completely perturbed low-rank matrix recovery. The paper that based on the restricted isometry property generalizes the investigation to a complete perturbation model thinking over not only noise but also perturbation, gives the restricted isometry property condition that guarantees the recovery of low-rank matrix and the corresponding reconstruction error bound. In particular, the analysis of the result reveals that in the case that p decreases 0 and a>1 for the complete perturbation and low-rank matrix, the condition is the optimal sufficient condition δ_2r<1<cit.>. The numerical experiments are conducted to show better performance, and provides outperformance of the nonconvex Schatten p-minimization method comparing with the convex nuclear norm minimization approach in the completely perturbed scenario.
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