Effect of errors in the system matrix on maximum a posteriori image reconstruction

Jinyi Qi, Ronald H. Huesman

Research output: Contribution to journalArticle

40 Citations (Scopus)

Abstract

Statistically based iterative image reconstruction methods have been developed for emission tomography. One important component in iterative image reconstruction is the system matrix, which defines the mapping from the image space to the data space. Several groups have demonstrated that an accurate system matrix can improve image quality in both single photon emission computed tomography (SPECT) and positron emission tomography (PET). While iterative methods are amenable to arbitrary and complicated system models, the true system response is never known exactly. In practice, one also has to sacrifice the accuracy of the system model because of limited computing and imaging resources. This paper analyses the effect of errors in the system matrix on iterative image reconstruction methods that are based on the maximum a posteriori principle. We derived an analytical expression for calculating artefacts in a reconstructed image that are caused by errors in the system matrix using the first-order Taylor series approximation. The theoretical expression is used to determine the required minimum accuracy of the system matrix in emission tomography. Computer simulations show that the theoretical results work reasonably well in low-noise situations.

Original languageEnglish (US)
Pages (from-to)3297-3312
Number of pages16
JournalPhysics in Medicine and Biology
Volume50
Issue number14
DOIs
StatePublished - Jul 21 2005

Fingerprint

Computer-Assisted Image Processing
image reconstruction
Image reconstruction
tomography
matrices
Tomography
Single-Photon Emission-Computed Tomography
Positron-Emission Tomography
Computer Simulation
Artifacts
Noise
Single photon emission computed tomography
Positron emission tomography
Taylor series
Iterative methods
low noise
Image quality
artifacts
positrons
resources

ASJC Scopus subject areas

  • Biomedical Engineering
  • Physics and Astronomy (miscellaneous)
  • Radiology Nuclear Medicine and imaging
  • Radiological and Ultrasound Technology

Cite this

Effect of errors in the system matrix on maximum a posteriori image reconstruction. / Qi, Jinyi; Huesman, Ronald H.

In: Physics in Medicine and Biology, Vol. 50, No. 14, 21.07.2005, p. 3297-3312.

Research output: Contribution to journalArticle

Qi, Jinyi ; Huesman, Ronald H. / Effect of errors in the system matrix on maximum a posteriori image reconstruction. In: Physics in Medicine and Biology. 2005 ; Vol. 50, No. 14. pp. 3297-3312.
@article{e1a40414ce2c42598fab160fbeefe8de,
title = "Effect of errors in the system matrix on maximum a posteriori image reconstruction",
abstract = "Statistically based iterative image reconstruction methods have been developed for emission tomography. One important component in iterative image reconstruction is the system matrix, which defines the mapping from the image space to the data space. Several groups have demonstrated that an accurate system matrix can improve image quality in both single photon emission computed tomography (SPECT) and positron emission tomography (PET). While iterative methods are amenable to arbitrary and complicated system models, the true system response is never known exactly. In practice, one also has to sacrifice the accuracy of the system model because of limited computing and imaging resources. This paper analyses the effect of errors in the system matrix on iterative image reconstruction methods that are based on the maximum a posteriori principle. We derived an analytical expression for calculating artefacts in a reconstructed image that are caused by errors in the system matrix using the first-order Taylor series approximation. The theoretical expression is used to determine the required minimum accuracy of the system matrix in emission tomography. Computer simulations show that the theoretical results work reasonably well in low-noise situations.",
author = "Jinyi Qi and Huesman, {Ronald H.}",
year = "2005",
month = "7",
day = "21",
doi = "10.1088/0031-9155/50/14/007",
language = "English (US)",
volume = "50",
pages = "3297--3312",
journal = "Physics in Medicine and Biology",
issn = "0031-9155",
publisher = "IOP Publishing Ltd.",
number = "14",

}

TY - JOUR

T1 - Effect of errors in the system matrix on maximum a posteriori image reconstruction

AU - Qi, Jinyi

AU - Huesman, Ronald H.

PY - 2005/7/21

Y1 - 2005/7/21

N2 - Statistically based iterative image reconstruction methods have been developed for emission tomography. One important component in iterative image reconstruction is the system matrix, which defines the mapping from the image space to the data space. Several groups have demonstrated that an accurate system matrix can improve image quality in both single photon emission computed tomography (SPECT) and positron emission tomography (PET). While iterative methods are amenable to arbitrary and complicated system models, the true system response is never known exactly. In practice, one also has to sacrifice the accuracy of the system model because of limited computing and imaging resources. This paper analyses the effect of errors in the system matrix on iterative image reconstruction methods that are based on the maximum a posteriori principle. We derived an analytical expression for calculating artefacts in a reconstructed image that are caused by errors in the system matrix using the first-order Taylor series approximation. The theoretical expression is used to determine the required minimum accuracy of the system matrix in emission tomography. Computer simulations show that the theoretical results work reasonably well in low-noise situations.

AB - Statistically based iterative image reconstruction methods have been developed for emission tomography. One important component in iterative image reconstruction is the system matrix, which defines the mapping from the image space to the data space. Several groups have demonstrated that an accurate system matrix can improve image quality in both single photon emission computed tomography (SPECT) and positron emission tomography (PET). While iterative methods are amenable to arbitrary and complicated system models, the true system response is never known exactly. In practice, one also has to sacrifice the accuracy of the system model because of limited computing and imaging resources. This paper analyses the effect of errors in the system matrix on iterative image reconstruction methods that are based on the maximum a posteriori principle. We derived an analytical expression for calculating artefacts in a reconstructed image that are caused by errors in the system matrix using the first-order Taylor series approximation. The theoretical expression is used to determine the required minimum accuracy of the system matrix in emission tomography. Computer simulations show that the theoretical results work reasonably well in low-noise situations.

UR - http://www.scopus.com/inward/record.url?scp=22244443384&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=22244443384&partnerID=8YFLogxK

U2 - 10.1088/0031-9155/50/14/007

DO - 10.1088/0031-9155/50/14/007

M3 - Article

VL - 50

SP - 3297

EP - 3312

JO - Physics in Medicine and Biology

JF - Physics in Medicine and Biology

SN - 0031-9155

IS - 14

ER -