REVIEW 1 cited by
Semiclassical sampling and discretization of certain linear inverse problems
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
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.
Forward citations
Cited by 1 Pith paper
-
Resolution analysis of inverting the generalized Radon transform from discrete data in $\mathbb R^3$
For a general class of 3D generalized Radon transforms, the resolution of reconstructed jump discontinuities from discrete data is an explicit edge profile determined by the interpolation kernel, with no non-local art...
Discussion (0). Continue with ORCID to comment.