  We study the problem of reconstructing a signal from its projection on a
subspace. The proposed signal reconstruction algorithms utilize a guiding
subspace that represents desired properties of reconstructed signals. We show
that optimal reconstructed signals belong to a convex bounded set, called the
"reconstruction" set. We also develop iterative algorithms, based on conjugate
gradient methods, to approximate optimal reconstructions with low memory and
computational costs. The effectiveness of the proposed approach is demonstrated
for image magnification, where the reconstructed image quality is shown to
exceed that of consistent and generalized reconstruction schemes.
