Sampling and Reconstruction in Distinct Subspaces Using Oblique Projections
Abstract
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.
Cite
@article{arxiv.1706.06444,
title = {Sampling and Reconstruction in Distinct Subspaces Using Oblique Projections},
author = {Peter Berger and Karlheinz Gröchenig and Gerald Matz},
journal= {arXiv preprint arXiv:1706.06444},
year = {2019}
}
Comments
30 pages, same title as arXiv:1312.1717 by the first two authors,otherwise little overlap