2018/11/03 by Stefanov, Plamen · 1 citation
#35A27 #35R30 #44A12 #94A20 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.1811.01240
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.