NON-UNIQUENESS OF THE RECONSTRUCTION FOR CONNECTED AND SIMPLY CONNECTED SETS IN THE PLANE BY THEIR FIXED#br#
FINITE PROJECTIONS

doi:10.1016/S0252-9602(12)60130-1

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (4): 1637-1646.doi: 10.1016/S0252-9602(12)60130-1

NON-UNIQUENESS OF THE RECONSTRUCTION FOR CONNECTED AND SIMPLY CONNECTED SETS IN THE PLANE BY THEIR FIXED#br# FINITE PROJECTIONS

Takashi Takiguchi

Department of Mathematics, National Defense Academy of Japan, Yokosuka, Kanagawa, 239-8686, Japan

收稿日期:2009-02-12 修回日期:2011-03-07 出版日期:2012-07-20 发布日期:2012-07-20

NON-UNIQUENESS OF THE RECONSTRUCTION FOR CONNECTED AND SIMPLY CONNECTED SETS IN THE PLANE BY THEIR FIXED#br# FINITE PROJECTIONS

Takashi Takiguchi

Department of Mathematics, National Defense Academy of Japan, Yokosuka, Kanagawa, 239-8686, Japan

Received:2009-02-12 Revised:2011-03-07 Online:2012-07-20 Published:2012-07-20

摘要/Abstract

摘要：

We discuss a problem to reconstruct the measurable sets in the plane from their fixed finite projections. In the main theorem, we construct an example of connected and simply connected polygons which are not uniquely reconstructed by their fixed finite projections. We also make a comparison between our main theorem and the known results on this problem.

关键词: Radon transform, inverse problem

Abstract:

Key words: Radon transform, inverse problem

中图分类号:

44A12

Takashi Takiguchi. NON-UNIQUENESS OF THE RECONSTRUCTION FOR CONNECTED AND SIMPLY CONNECTED SETS IN THE PLANE BY THEIR FIXED#br# FINITE PROJECTIONS[J]. 数学物理学报(英文版), 2012, 32(4): 1637-1646.

Takashi Takiguchi. NON-UNIQUENESS OF THE RECONSTRUCTION FOR CONNECTED AND SIMPLY CONNECTED SETS IN THE PLANE BY THEIR FIXED#br# FINITE PROJECTIONS[J]. Acta mathematica scientia,Series B, 2012, 32(4): 1637-1646.

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NON-UNIQUENESS OF THE RECONSTRUCTION FOR CONNECTED AND SIMPLY CONNECTED SETS IN THE PLANE BY THEIR FIXED#br# FINITE PROJECTIONS

NON-UNIQUENESS OF THE RECONSTRUCTION FOR CONNECTED AND SIMPLY CONNECTED SETS IN THE PLANE BY THEIR FIXED#br# FINITE PROJECTIONS

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