(Subscript[M, low  rank])=[U,Σ,V]=(Underscript[arg min , U,Σ,V]){((\[LeftDoubleBracketingBar](Subscript[S, noisy])-U Σ (V^T)\[RightDoubleBracketingBar])^2)+(Subscript[a, u])\[LeftDoubleBracketingBar](Subscript[B, u])U\[RightDoubleBracketingBar]+(Subscript[a, v])\[LeftDoubleBracketingBar](Subscript[B, v])V\[RightDoubleBracketingBar]}