Motion compensated local tomography

    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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