Inversion of the attenuated radon transform for non-parallel geometries

Tianfang Li; Jiangsheng You; Junhai Wen; Zhengrong Liang

Inversion of the attenuated radon transform for non-parallel geometries

Tianfang Li^*
, Jiangsheng You
, Junhai Wen
, Zhengrong Liang

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › peer-review

1 Citation (Scopus)

Abstract

In this work, we first introduced a reorganized form of the Novikov's inversion formula for the attenuated Radon transform with parallel-beam geometry which utilizes the conventional filters (such as the Shepp-Logan, Manning, etc.) to simplify image reconstruction procedures. Then we developed an accurate reconstruction method for non-parallel beam geometries. The method contains three major steps: (1) one-dimensional rebinning using phase-shifting technique, (2) performing non-uniform Hubert transform, and (3) applying the reorganized Novikov's formula. Numerical evaluations demonstrated its computational efficiency and sound stability to different levels of Poisson noise. It also seemed to be very robust to different settings of fan-beam geometry from very long to very short focal lengths without affecting the reconstruction accuracy.

Original language	English
Article number	M2-189
Pages (from-to)	2525-2529
Number of pages	5
Journal	IEEE Nuclear Science Symposium Conference Record
Volume	4
Publication status	Published - 2004
Externally published	Yes
Event	2004 Nuclear Science Symposium, Medical Imaging Conference, Symposium on Nuclear Power Systems and the 14th International Workshop on Room Temperature Semiconductor X- and Gamma- Ray Detectors - Rome, Italy Duration: 16 Oct 2004 → 22 Oct 2004

Cite this

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title = "Inversion of the attenuated radon transform for non-parallel geometries",

abstract = "In this work, we first introduced a reorganized form of the Novikov's inversion formula for the attenuated Radon transform with parallel-beam geometry which utilizes the conventional filters (such as the Shepp-Logan, Manning, etc.) to simplify image reconstruction procedures. Then we developed an accurate reconstruction method for non-parallel beam geometries. The method contains three major steps: (1) one-dimensional rebinning using phase-shifting technique, (2) performing non-uniform Hubert transform, and (3) applying the reorganized Novikov's formula. Numerical evaluations demonstrated its computational efficiency and sound stability to different levels of Poisson noise. It also seemed to be very robust to different settings of fan-beam geometry from very long to very short focal lengths without affecting the reconstruction accuracy.",

author = "Tianfang Li and Jiangsheng You and Junhai Wen and Zhengrong Liang",

year = "2004",

language = "English",

volume = "4",

pages = "2525--2529",

journal = "IEEE Nuclear Science Symposium Conference Record",

issn = "1095-7863",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

note = "2004 Nuclear Science Symposium, Medical Imaging Conference, Symposium on Nuclear Power Systems and the 14th International Workshop on Room Temperature Semiconductor X- and Gamma- Ray Detectors ; Conference date: 16-10-2004 Through 22-10-2004",

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TY - JOUR

T1 - Inversion of the attenuated radon transform for non-parallel geometries

AU - Li, Tianfang

AU - You, Jiangsheng

AU - Wen, Junhai

AU - Liang, Zhengrong

PY - 2004

Y1 - 2004

N2 - In this work, we first introduced a reorganized form of the Novikov's inversion formula for the attenuated Radon transform with parallel-beam geometry which utilizes the conventional filters (such as the Shepp-Logan, Manning, etc.) to simplify image reconstruction procedures. Then we developed an accurate reconstruction method for non-parallel beam geometries. The method contains three major steps: (1) one-dimensional rebinning using phase-shifting technique, (2) performing non-uniform Hubert transform, and (3) applying the reorganized Novikov's formula. Numerical evaluations demonstrated its computational efficiency and sound stability to different levels of Poisson noise. It also seemed to be very robust to different settings of fan-beam geometry from very long to very short focal lengths without affecting the reconstruction accuracy.

AB - In this work, we first introduced a reorganized form of the Novikov's inversion formula for the attenuated Radon transform with parallel-beam geometry which utilizes the conventional filters (such as the Shepp-Logan, Manning, etc.) to simplify image reconstruction procedures. Then we developed an accurate reconstruction method for non-parallel beam geometries. The method contains three major steps: (1) one-dimensional rebinning using phase-shifting technique, (2) performing non-uniform Hubert transform, and (3) applying the reorganized Novikov's formula. Numerical evaluations demonstrated its computational efficiency and sound stability to different levels of Poisson noise. It also seemed to be very robust to different settings of fan-beam geometry from very long to very short focal lengths without affecting the reconstruction accuracy.

UR - https://www.scopus.com/pages/publications/23844503997

M3 - Conference article

AN - SCOPUS:23844503997

SN - 1095-7863

VL - 4

SP - 2525

EP - 2529

JO - IEEE Nuclear Science Symposium Conference Record

JF - IEEE Nuclear Science Symposium Conference Record

M1 - M2-189

T2 - 2004 Nuclear Science Symposium, Medical Imaging Conference, Symposium on Nuclear Power Systems and the 14th International Workshop on Room Temperature Semiconductor X- and Gamma- Ray Detectors

Y2 - 16 October 2004 through 22 October 2004

ER -

Inversion of the attenuated radon transform for non-parallel geometries

Abstract

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