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This work studies the Generalized Singular Value Thresholding (GSVT) operator Prox_g^σ(·), Prox_g^σ(B)=_X∑_i=1^mg(σ_i(X)) + 1/2||X-B||_F^2, associated with a nonconvex function g defined on the singular values of X. We prove that GSVT can be obtained by performing the proximal operator of g (denoted as Prox_g(·)) on the singular values since Prox_g(·) is monotone when g is lower bounded. If the nonconvex g satisfies some conditions (many popular nonconvex surrogate functions, e.g., ℓ_p-norm,arXiv:1412.2231v2 fatcat:vce6u4i3cvho7eohu3pwg4m66a