with Y 1ptq " X ptq ´Φptq Y {ρ, and the singular value thresholding operator ] D σ acts on A " Updiagptσ i uq 1ďiďr qV J , with the reduced SVD, as A " Updiagp ␣ S σ pσ i q ( 1ďiďr qqV J . S σ pxq " sgnpxqmaxp|x|´σq is the soft-thresholding operator with maxpb, 0q that takes b if b ą 0 and 0 otherwise. The role of updating Y is to approximate the underlying signal to have a reduced nuclear norm, which is the convex relaxation of the rank, as assumed in (A3).