### Abstract

Purpose: To investigate the correlation and stationarity of noise in volumetric computed tomography (CT) using the local discrete noise-power spectrum (NPS) and off-diagonal elements of the covariance matrix of the discrete Fourier transform of noise-only images (denoted Σ_{DFT}). Experimental conditions were varied to affect noise correlation and stationarity, the effects were quantified in terms of the NPS and Σ_{DFT}, and practical considerations in CT performance characterization were identified. Methods: Cone-beam CT (CBCT) images were acquired using a benchtop system comprising an x-ray tube and flat-panel detector for a range of acquisition techniques (e.g., dose and x-ray scatter) and three phantom configurations hypothesized to impart distinct effects on the NPS and Σ_{DFT}: (A) air, (B) a 20-cm-diameter water cylinder with a bowtie filter, and (C) the cylinder without a bowtie filter. The NPS and off-diagonal elements of the Σ_{DFT} were analyzed as a function of position within the reconstructions. Results: The local NPS varied systematically throughout the axial plane in a manner consistent with changes in fluence transmitted to the detector and view sampling effects. Variability in fluence was manifest in the NPS magnitude-e.g., a factor of ∼2 variation in NPS magnitude within the axial plane for case C (cylinder without bowtie), compared to nearly constant NPS magnitude for case B (bowtie filter matched to the cylinder). View sampling effects were most prominent in case A (air) where the variance increased at greater distance from the center of reconstruction and in case C (cylinder) where the NPS exhibited correlations in the radial direction. The effects of detector lag were observed as azimuthal correlation. The cylinder (without bowtie) had the strongest nonstationarity because of the larger variability in fluence transmitted to the detector. The diagonal elements of the Σ_{DFT} were equivalent to the NPS estimated from the periodogram, and the average off-diagonal elements of the Σ_{DFT} exhibited amplitude of ∼1 of the NPS for the experimental conditions investigated. Furthermore, the off-diagonal elements demonstrated fairly long tails of nearly constant amplitude, with magnitude somewhat reduced for experimental conditions associated with greater stationarity (viz., lower Σ_{DFT} tails for cases A and B in comparison to case C). Conclusions: Volumetric CT exhibits nonstationarity in the NPS as hypothesized in relation to fluence uniformity and view sampling. Measurement of the NPS should seek to minimize such changes in noise correlations and include careful reporting of experimental conditions (e.g., phantom design and use of a bowtie filter) and spatial dependence (e.g., analysis at fixed radius within a phantom). Off-diagonal elements of the Σ_{DFT} similarly depend on experimental conditions and can be readily computed from the same data as the NPS. This work begins to check assumptions in NPS analysis examine the extent to which NPS is an appropriate descriptor of noise correlations, and investigate the magnitude of off-diagonal elements of the Σ_{DFT}. While the magnitude of such off-diagonal elements appears to be low, their cumulative effect on space-variant detectability remains to be investigated-e.g., using task-specific figures of merit.

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

Pages (from-to) | 3240-3252 |

Number of pages | 13 |

Journal | Medical Physics |

Volume | 39 |

Issue number | 6 |

DOIs | |

State | Published - Jun 2012 |

### Fingerprint

### Keywords

- computed tomography
- cone-beam CT
- covariance matrix
- image quality
- noise-power spectrum
- stationarity

### ASJC Scopus subject areas

- Biophysics
- Radiology Nuclear Medicine and imaging

### Cite this

*Medical Physics*,

*39*(6), 3240-3252. https://doi.org/10.1118/1.4705354

**Beyond noise power in 3D computed tomography : The local NPS and off-diagonal elements of the Fourier domain covariance matrix.** / Pineda, Angel R.; Tward, Daniel J.; Gonzalez, Antonio; Siewerdsen, Jeff.

Research output: Contribution to journal › Article

*Medical Physics*, vol. 39, no. 6, pp. 3240-3252. https://doi.org/10.1118/1.4705354

}

TY - JOUR

T1 - Beyond noise power in 3D computed tomography

T2 - The local NPS and off-diagonal elements of the Fourier domain covariance matrix

AU - Pineda, Angel R.

AU - Tward, Daniel J.

AU - Gonzalez, Antonio

AU - Siewerdsen, Jeff

PY - 2012/6

Y1 - 2012/6

N2 - Purpose: To investigate the correlation and stationarity of noise in volumetric computed tomography (CT) using the local discrete noise-power spectrum (NPS) and off-diagonal elements of the covariance matrix of the discrete Fourier transform of noise-only images (denoted ΣDFT). Experimental conditions were varied to affect noise correlation and stationarity, the effects were quantified in terms of the NPS and ΣDFT, and practical considerations in CT performance characterization were identified. Methods: Cone-beam CT (CBCT) images were acquired using a benchtop system comprising an x-ray tube and flat-panel detector for a range of acquisition techniques (e.g., dose and x-ray scatter) and three phantom configurations hypothesized to impart distinct effects on the NPS and ΣDFT: (A) air, (B) a 20-cm-diameter water cylinder with a bowtie filter, and (C) the cylinder without a bowtie filter. The NPS and off-diagonal elements of the ΣDFT were analyzed as a function of position within the reconstructions. Results: The local NPS varied systematically throughout the axial plane in a manner consistent with changes in fluence transmitted to the detector and view sampling effects. Variability in fluence was manifest in the NPS magnitude-e.g., a factor of ∼2 variation in NPS magnitude within the axial plane for case C (cylinder without bowtie), compared to nearly constant NPS magnitude for case B (bowtie filter matched to the cylinder). View sampling effects were most prominent in case A (air) where the variance increased at greater distance from the center of reconstruction and in case C (cylinder) where the NPS exhibited correlations in the radial direction. The effects of detector lag were observed as azimuthal correlation. The cylinder (without bowtie) had the strongest nonstationarity because of the larger variability in fluence transmitted to the detector. The diagonal elements of the ΣDFT were equivalent to the NPS estimated from the periodogram, and the average off-diagonal elements of the ΣDFT exhibited amplitude of ∼1 of the NPS for the experimental conditions investigated. Furthermore, the off-diagonal elements demonstrated fairly long tails of nearly constant amplitude, with magnitude somewhat reduced for experimental conditions associated with greater stationarity (viz., lower ΣDFT tails for cases A and B in comparison to case C). Conclusions: Volumetric CT exhibits nonstationarity in the NPS as hypothesized in relation to fluence uniformity and view sampling. Measurement of the NPS should seek to minimize such changes in noise correlations and include careful reporting of experimental conditions (e.g., phantom design and use of a bowtie filter) and spatial dependence (e.g., analysis at fixed radius within a phantom). Off-diagonal elements of the ΣDFT similarly depend on experimental conditions and can be readily computed from the same data as the NPS. This work begins to check assumptions in NPS analysis examine the extent to which NPS is an appropriate descriptor of noise correlations, and investigate the magnitude of off-diagonal elements of the ΣDFT. While the magnitude of such off-diagonal elements appears to be low, their cumulative effect on space-variant detectability remains to be investigated-e.g., using task-specific figures of merit.

AB - Purpose: To investigate the correlation and stationarity of noise in volumetric computed tomography (CT) using the local discrete noise-power spectrum (NPS) and off-diagonal elements of the covariance matrix of the discrete Fourier transform of noise-only images (denoted ΣDFT). Experimental conditions were varied to affect noise correlation and stationarity, the effects were quantified in terms of the NPS and ΣDFT, and practical considerations in CT performance characterization were identified. Methods: Cone-beam CT (CBCT) images were acquired using a benchtop system comprising an x-ray tube and flat-panel detector for a range of acquisition techniques (e.g., dose and x-ray scatter) and three phantom configurations hypothesized to impart distinct effects on the NPS and ΣDFT: (A) air, (B) a 20-cm-diameter water cylinder with a bowtie filter, and (C) the cylinder without a bowtie filter. The NPS and off-diagonal elements of the ΣDFT were analyzed as a function of position within the reconstructions. Results: The local NPS varied systematically throughout the axial plane in a manner consistent with changes in fluence transmitted to the detector and view sampling effects. Variability in fluence was manifest in the NPS magnitude-e.g., a factor of ∼2 variation in NPS magnitude within the axial plane for case C (cylinder without bowtie), compared to nearly constant NPS magnitude for case B (bowtie filter matched to the cylinder). View sampling effects were most prominent in case A (air) where the variance increased at greater distance from the center of reconstruction and in case C (cylinder) where the NPS exhibited correlations in the radial direction. The effects of detector lag were observed as azimuthal correlation. The cylinder (without bowtie) had the strongest nonstationarity because of the larger variability in fluence transmitted to the detector. The diagonal elements of the ΣDFT were equivalent to the NPS estimated from the periodogram, and the average off-diagonal elements of the ΣDFT exhibited amplitude of ∼1 of the NPS for the experimental conditions investigated. Furthermore, the off-diagonal elements demonstrated fairly long tails of nearly constant amplitude, with magnitude somewhat reduced for experimental conditions associated with greater stationarity (viz., lower ΣDFT tails for cases A and B in comparison to case C). Conclusions: Volumetric CT exhibits nonstationarity in the NPS as hypothesized in relation to fluence uniformity and view sampling. Measurement of the NPS should seek to minimize such changes in noise correlations and include careful reporting of experimental conditions (e.g., phantom design and use of a bowtie filter) and spatial dependence (e.g., analysis at fixed radius within a phantom). Off-diagonal elements of the ΣDFT similarly depend on experimental conditions and can be readily computed from the same data as the NPS. This work begins to check assumptions in NPS analysis examine the extent to which NPS is an appropriate descriptor of noise correlations, and investigate the magnitude of off-diagonal elements of the ΣDFT. While the magnitude of such off-diagonal elements appears to be low, their cumulative effect on space-variant detectability remains to be investigated-e.g., using task-specific figures of merit.

KW - computed tomography

KW - cone-beam CT

KW - covariance matrix

KW - image quality

KW - noise-power spectrum

KW - stationarity

UR - http://www.scopus.com/inward/record.url?scp=84863533966&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84863533966&partnerID=8YFLogxK

U2 - 10.1118/1.4705354

DO - 10.1118/1.4705354

M3 - Article

C2 - 22755707

AN - SCOPUS:84863533966

VL - 39

SP - 3240

EP - 3252

JO - Medical Physics

JF - Medical Physics

SN - 0094-2405

IS - 6

ER -