By using the relative derived categories, we prove that if an Artin algebra
$A$ has a module $T$ with ${\rm inj.dim}T<\infty$ such that $^\perp T$ is
finite, then the bounded derived category $D^b(A\mbox{-}{\rm mod})$ admits a
categorical resolution in the sense of [Kuz], and a categorical
desingularization in the sense of [BO]. For CM-finite Gorenstein algebra, such
a categorical resolution is weakly crepant. The similar results hold also for
$D^b(A\mbox{-}{\rm Mod})$.Comment: 23 page