  We introduce a geometric realization of noncommutative singularity
resolutions. To do this, we first present a new conjectural method of obtaining
conventional resolutions using coordinate rings of matrix-valued functions. We
verify this conjecture for all cyclic quotient surface singularities, the
Kleinian D_n and E_6 surface singularities, the conifold singularity, and a
non-isolated singularity, using appropriate quiver algebras. This conjecture
provides a possible new generalization of the classical McKay correspondence.
Then, using symplectic reduction within these rings, we obtain new,
non-conventional resolutions that are hidden if only commutative functions are
considered. Geometrically, these non-conventional resolutions result from
shrinking exceptional loci to ramified (non-Azumaya) point-like spheres.
