  We study reconstruction operators on a Hilbert space that are exact on a
given reconstruction subspace. Among those the reconstruction operator obtained
by the least squares fit has the smallest operator norm, and therefore is most
stable with respect to noisy measurements. We then construct the operator with
the smallest possible quasi-optimality constant, which is the most stable with
respect to a systematic error appearing before the sampling process (model
uncertainty). We describe how to vary continuously between the two
reconstruction methods, so that we can trade stability for quasi-optimality. As
an application we study the reconstruction of a compactly supported function
from nonuniform samples of its Fourier transform.
