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Title: Sampling linear inverse problems with noise
We study the effect of additive noise to the inversion of FIOs associated to a diffeomorphic canonical relation. We use the microlocal defect measures to measure the power spectrum of the noise in the phase space and analyze how that power spectrum is transformed under the inversion. In general, white noise, for example, is mapped to noise depending on the position and on the direction. In particular, we compute the standard deviation, locally, of the noise added to the inversion as a function of the standard deviation of the noise added to the data. As an example, we study the Radon transform in the plane in parallel and fan-beam coordinates, and present numerical examples.  more » « less
Award ID(s):
1900475
PAR ID:
10450566
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Asymptotic Analysis
Volume:
132
Issue:
3-4
ISSN:
0921-7134
Page Range / eLocation ID:
331 to 382
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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