### Abstract

Statistical image reconstruction (SIR) is a promising approach to reducing radiation dose in clinical computerized tomography (CT) scans. Clinical CT scanners use energy-integrating detectors. The CT signal follows a compound Poisson distribution, its probability density function (PDF) does not have an analytical form hence cannot be used in an SIR method. The goal of this work is to quantify the effects of using an approximate statistical assumption in SIR methods for clinical CT applications. We apply a pseudo-Ideal Observer (pIO) to simulated CT projection data of the fanbeam geometry at different dose levels. The simulation models the polychromatic X-ray tube spectrum, the effects of the bowtie filter, and the energy-integrating detectors. The pIO uses a pseudo likelihood function (pLF) to calculate the pseudo likelihood ratio, which is the decision variable used by the pIO in a binary detection task. The pLF is an approximation to the true LF of the underlying data. The pIO has inferior performance than the IO unless the pLF coincides with the LF; this performance difference quantifies the closeness between the pseudo likelihood and the exact one. Using lesion detectability in a signal known exactly, background known exactly binary detection task as a figure-of-merit, our results show that at down to 0.1% of a reference tube current level I_{0} , the pIO that uses a Poisson approximation, or a matched variance Gaussian approximation in either the transmission or the line integral domain, achieves 99% the performance of the IO. The constant variance Gaussian approximation has only 70%-80% of the IO performance. At tube currents lower than 0.1% I_{0}, the performance difference is more substantial. We conclude that at current clinical dose levels, it is important to account for the mean-dependent variance in CT projection data in SIR problem formulation, the exact PDF of the CT signal is not as important.

Original language | English (US) |
---|---|

Article number | 6588321 |

Pages (from-to) | 61-73 |

Number of pages | 13 |

Journal | IEEE Transactions on Medical Imaging |

Volume | 33 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2014 |

### Fingerprint

### Keywords

- Clinical X-ray computerized tomography (CT) systems
- compound Poisson distribution
- energy-integrating detectors
- ideal observer (IO)
- maximum-likelihood estimate
- pseudo-likelihood
- statistical image reconstruction

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Computer Science Applications
- Radiological and Ultrasound Technology
- Software

### Cite this

**Quantifying the importance of the statistical assumption in statistical X-ray CT image reconstruction.** / Xu, Jingyan; Tsui, Benjamin.

Research output: Contribution to journal › Article

*IEEE Transactions on Medical Imaging*, vol. 33, no. 1, 6588321, pp. 61-73. https://doi.org/10.1109/TMI.2013.2280383

}

TY - JOUR

T1 - Quantifying the importance of the statistical assumption in statistical X-ray CT image reconstruction

AU - Xu, Jingyan

AU - Tsui, Benjamin

PY - 2014/1

Y1 - 2014/1

N2 - Statistical image reconstruction (SIR) is a promising approach to reducing radiation dose in clinical computerized tomography (CT) scans. Clinical CT scanners use energy-integrating detectors. The CT signal follows a compound Poisson distribution, its probability density function (PDF) does not have an analytical form hence cannot be used in an SIR method. The goal of this work is to quantify the effects of using an approximate statistical assumption in SIR methods for clinical CT applications. We apply a pseudo-Ideal Observer (pIO) to simulated CT projection data of the fanbeam geometry at different dose levels. The simulation models the polychromatic X-ray tube spectrum, the effects of the bowtie filter, and the energy-integrating detectors. The pIO uses a pseudo likelihood function (pLF) to calculate the pseudo likelihood ratio, which is the decision variable used by the pIO in a binary detection task. The pLF is an approximation to the true LF of the underlying data. The pIO has inferior performance than the IO unless the pLF coincides with the LF; this performance difference quantifies the closeness between the pseudo likelihood and the exact one. Using lesion detectability in a signal known exactly, background known exactly binary detection task as a figure-of-merit, our results show that at down to 0.1% of a reference tube current level I0 , the pIO that uses a Poisson approximation, or a matched variance Gaussian approximation in either the transmission or the line integral domain, achieves 99% the performance of the IO. The constant variance Gaussian approximation has only 70%-80% of the IO performance. At tube currents lower than 0.1% I0, the performance difference is more substantial. We conclude that at current clinical dose levels, it is important to account for the mean-dependent variance in CT projection data in SIR problem formulation, the exact PDF of the CT signal is not as important.

AB - Statistical image reconstruction (SIR) is a promising approach to reducing radiation dose in clinical computerized tomography (CT) scans. Clinical CT scanners use energy-integrating detectors. The CT signal follows a compound Poisson distribution, its probability density function (PDF) does not have an analytical form hence cannot be used in an SIR method. The goal of this work is to quantify the effects of using an approximate statistical assumption in SIR methods for clinical CT applications. We apply a pseudo-Ideal Observer (pIO) to simulated CT projection data of the fanbeam geometry at different dose levels. The simulation models the polychromatic X-ray tube spectrum, the effects of the bowtie filter, and the energy-integrating detectors. The pIO uses a pseudo likelihood function (pLF) to calculate the pseudo likelihood ratio, which is the decision variable used by the pIO in a binary detection task. The pLF is an approximation to the true LF of the underlying data. The pIO has inferior performance than the IO unless the pLF coincides with the LF; this performance difference quantifies the closeness between the pseudo likelihood and the exact one. Using lesion detectability in a signal known exactly, background known exactly binary detection task as a figure-of-merit, our results show that at down to 0.1% of a reference tube current level I0 , the pIO that uses a Poisson approximation, or a matched variance Gaussian approximation in either the transmission or the line integral domain, achieves 99% the performance of the IO. The constant variance Gaussian approximation has only 70%-80% of the IO performance. At tube currents lower than 0.1% I0, the performance difference is more substantial. We conclude that at current clinical dose levels, it is important to account for the mean-dependent variance in CT projection data in SIR problem formulation, the exact PDF of the CT signal is not as important.

KW - Clinical X-ray computerized tomography (CT) systems

KW - compound Poisson distribution

KW - energy-integrating detectors

KW - ideal observer (IO)

KW - maximum-likelihood estimate

KW - pseudo-likelihood

KW - statistical image reconstruction

UR - http://www.scopus.com/inward/record.url?scp=84892387025&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84892387025&partnerID=8YFLogxK

U2 - 10.1109/TMI.2013.2280383

DO - 10.1109/TMI.2013.2280383

M3 - Article

C2 - 24001989

AN - SCOPUS:84892387025

VL - 33

SP - 61

EP - 73

JO - IEEE Transactions on Medical Imaging

JF - IEEE Transactions on Medical Imaging

SN - 0278-0062

IS - 1

M1 - 6588321

ER -