High-resolution signal recovery via generalized sampling and functional principal component analysis

In this paper, we introduce a computational framework for recovering high-resolution approximation of an unknown function from its low-resolution indirect measurements as well training observations by merging the frameworks generalized sampling and functional principal component analysis. particular, increase signal resolution via data-driven approach, which models interest realization random field leverages set generated same underlying process. We study performance resulting estimation procedure show that recovery is indeed possible provided appropriate low rank angle conditions hold sufficiently large relative to desired resolution. Moreover, size can be reduced leveraging sparse representations components. Furthermore, effectiveness proposed reconstruction illustrated various numerical examples.