The purpose of this paper is to report on recent approaches to reconstruction problems based on analog, or in other words, infinite-dimensional, image and signal models. We describe three main contributions to this problem. First, linear reconstructions from sampled measurements via so-called generalized sampling (GS). Second, the extension of generalized sampling to inverse and ill-posed problems. And third, the combination of generalized sampling with sparse recovery techniques. This final contribution leads to a theory and set of methods for infinite-dimensional compressed sensing, or as we shall also refer to it, compressed sensing over the continuum.
@article{arxiv.1310.1141,
title = {Generalized sampling: stable reconstructions, inverse problems and compressed sensing over the continuum},
author = {Ben Adcock and Anders Hansen and Bogdan Roman and Gerd Teschke},
journal= {arXiv preprint arXiv:1310.1141},
year = {2013}
}