A Local Approach To Resolution Analysis Of Image Reconstruction In Tomography

Keywords

Dynamic imaging; Reconstruction; Resolution

Abstract

We propose a novel approach to analyzing resolution of tomographic reconstruction. Instead of following a conventional approach to obtain a global accuracy estimate, we investigate how the reconstructed function fϵ approximates the singularities of the original object f. The data is a discretized 2D Radon transform of f. The object could be static or change with time (dynamic tomography). Suppose the step-sizes along the angular and affine variables are O(ϵ). We pick a point x0, where f has a jump singularity, and obtain the leading singular behavior of fϵ in an O(ϵ)-neighborhood of x0 as ϵ → 0. It turns out that the limiting behavior of fϵ depends only on the data microlocally near the singularity being reconstructed. This significantly simplifies the analysis and allows us to investigate complicated settings, e.g., dynamic tomography. Also, our resolution analysis is algorithm-specific - the same approach can be used for analyzing and optimizing various linear reconstruction algorithms. We present the results of numerical experiments in the static and dynamic cases. These results demonstrate an excellent agreement between predicted and actual behaviors of fϵ near a jump discontinuity of f.

Publication Date

1-1-2017

Publication Title

SIAM Journal on Applied Mathematics

Volume

77

Issue

5

Number of Pages

1706-1732

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1137/17M1112108

Socpus ID

85033469187 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85033469187

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