Sampling linear inverse problems with noise

2020/11/26 by Stefanov, Plamen, Tindel, Samy · 2 citations
#35R30 #44A12 #60H40 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2011.13489

Abstract

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 and analyze how that power spectrum is transformed under the inversion. In particular, we compute the standard deviation 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.

Cited by

• Local Characterization of Noise in Iterative Reconstruction of the Generalized Radon Transform
• Sampling theorems for inverse problems on Riemannian manifolds

Related

• Semiclassical sampling and discretization of certain linear inverse problems
• Local reconstruction analysis of inverting the Radon transform in the plane from noisy discrete data
• Inverse Problems with Invariant Multiscale Statistics
• Regularization of linear inverse problems with irregular noise using embedding operators
• Sampling theorems for inverse problems on Riemannian manifolds