摘要
In this paper, a sufficient condition is obtained to ensure the stable recovery(ε≠ 0) or exact recovery(ε = 0) of all r-rank matrices X ∈ Rm×nfrom b = A(X) + z via nonconvex Schatten p-minimization for anyδ4r∈ [3～(1/2))2, 1). Moreover, we determine the range of parameter p with any given δ4r∈ [(3～(1/2))/22, 1). In fact, for any given δ4r∈ [3～(1/2))2, 1), p ∈(0, 2(1- δ4r)] suffices for the stable recovery or exact recovery of all r-rank matrices.
In this paper, a sufficient condition is obtained to ensure the stable recovery（ε ≠ 0） or exact recovery（ε = 0） of all r-rank matrices X ∈ Rm×nfrom b = A（X） ＋ z via nonconvex Schatten p-minimization for anyδ4r∈ [3～（1/2））2, 1）. Moreover, we determine the range of parameter p with any given δ4r∈ [（3～（1/2））/22, 1）. In fact, for any given δ4r∈ [3～（1/2））2, 1）, p ∈（0, 2（1- δ4r）] suffices for the stable recovery or exact recovery of all r-rank matrices.
基金
supported by National Natural Science Foundation of China(Grant Nos.11271050 and 11371183)
Beijing Center for Mathematics and Information Interdisciplinary Sciences
