Unifying two results of Orlov on singularity categories

Let \mathbbX\mathbb{X} be a separated Noetherian scheme of finite Krull dimension which has enough locally free sheaves of finite rank and let U í \mathbbXU\subseteq \mathbb{X} be an open subscheme. We prove that the singularity category of U is triangle equivalent to the Verdier quotient triangulated category of the singularity category of \mathbbX\mathbb{X} with respect to the thick triangulated subcategory generated by sheaves supported in the complement of U. The result unifies two results of Orlov. We also prove a noncommutative version of this result.