Title

Motion compensated local tomography

Authors

Authors

A. Katsevich

Comments

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Abbreviated Journal Title

Inverse Probl.

Keywords

CONE-BEAM RECONSTRUCTION; MULTISLICE SPIRAL CT; COMPUTED-TOMOGRAPHY; IMAGE-RECONSTRUCTION; SPLIT METHOD; TRANSFORM; HEART; FIELD; Mathematics, Applied; Physics, Mathematical

Abstract

In this paper we develop local tomography (LT) for image reconstruction from motion contaminated data. It is assumed that motion is known. We propose a new LT function f(Lambda), which is related to an original object f via an operator B: f(Lambda) = Bf. Because of motion, B may fail to be a pseudo-differential operator (PDO). We obtain the conditions that guarantee that B is a PDO. Under these conditions, similarly to the classical LT in R(2), B is a PDO of order 1. Computation of f(Lambda) depends on a weight function Phi. We show that Phi can be chosen in such a way that the operator B has principal symbol vertical bar xi vertical bar. This result has an interesting corollary for conventional exact reconstruction. It suggests a novel frequency-split approach to finding f from motion contaminated data. In practice tomographic data are discrete, and derivatives are usually replaced by their mollified analogs. We consider how mollification affects the singularities of the LT function f(Lambda). Using this approach we develop an algorithm for finding values of jumps of f using LT. We also consider various aspects of numerical implementation of LT and show the results of numerical experiments.

Journal Title

Inverse Problems

Volume

24

Issue/Number

4

Publication Date

1-1-2008

Document Type

Article

Language

English

First Page

21

WOS Identifier

WOS:000257837900012

ISSN

0266-5611

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