Semiclassical sampling and discretization of certain linear inverse problems

Plamen Stefanov

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arXiv · 1811.01240

Semiclassical sampling and discretization of certain linear inverse problems

Plamen Stefanov

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Abstract

We study sampling of Fourier Integral Operators $A$ at rates $sh$ with $s$ fixed and $h$ a small parameter. We show that the Nyquist sampling limit of $Af$ and $f$ are related by the canonical relation of $A$ using semiclassical analysis. We apply this analysis to the Radon transform in the parallel and the fan-beam coordinates. We explain and illustrate the optimal sampling rates for $Af$, the aliasing artifacts, and the effect of averaging (blurring) the data $Af$. We prove a Weyl type of estimate on the minimal number of sampling points to recover $f$ stably in terms of the volume of its semiclassical wave front set.

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Plamen Stefanov. 2018-11-03. Semiclassical sampling and discretization of certain linear inverse problems. https://arxiv.org/abs/1811.01240

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