Generalized Sampling and Infinite-Dimensional Compressed Sensing
@article{Adcock2016GeneralizedSA,
title={Generalized Sampling and Infinite-Dimensional Compressed Sensing},
author={B. Adcock and A. Hansen},
journal={Foundations of Computational Mathematics},
year={2016},
volume={16},
pages={1263-1323}
}We introduce and analyze a framework and corresponding method for compressed sensing in infinite dimensions. This extends the existing theory from finite-dimensional vector spaces to the case of separable Hilbert spaces. We explain why such a new theory is necessary by demonstrating that existing finite-dimensional techniques are ill suited for solving a number of key problems. This work stems from recent developments in generalized sampling theorems for classical (Nyquist rate) sampling that… CONTINUE READING
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