Stable recovery of low-rank matrix via nonconvex Schatten p-minimization

Abstract

In this paper, a sufficient condition is obtained to ensure the stable recovery ( ∈ ≠ 0) or exact recovery ( ∈ = 0) of all r -rank matrices X ∈ R m×n from b = A ( X ) + z via nonconvex Schatten p-minimization for any δ 4 r ∈ [√3/2 , 1). Moreover, we determine the range of parameter p with any given δ 4 r ∈ [√3/2 , 1). In fact, for any given δ 4 r ∈ [√3/2 , 1), p ∈ (0, 2(1 - δ 4 r )] suffices for the stable recovery or exact recovery of all r -rank matrices.