Analysis of x-ray computed tomography images using the noise power spectrum and autocorrelation function

Faulkner, K.; Moores, Brian

doi:10.1088/0031-9155/29/11/003

Cited by 45 publications

(44 citation statements)

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“…A wealth of literature has been devoted to studying the noise characteristics of xray computed tomography (CT) in terms of the pixel variance, spatial domain covariance matrix, or Fourier domain noise-power spectrum (NPS). [1][2][3][4][5][6] Moreover, it is generally accepted that image quality should be defined with respect to the imaging task, 7,8 where detectability is calculated to account for noise, spatial resolution as well as the task function and observer model. Such task-based frameworks are increasingly employed in system design, performance assessment, and optimization.…”

Section: Introductionmentioning

confidence: 99%

Task‐based detectability in CT image reconstruction by filtered backprojection and penalized likelihood estimation

et al. 2014

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Purpose: Nonstationarity is an important aspect of imaging performance in CT and cone-beam CT (CBCT), especially for systems employing iterative reconstruction. This work presents a theoretical framework for both filtered-backprojection (FBP) and penalized-likelihood (PL) reconstruction that includes explicit descriptions of nonstationary noise, spatial resolution, and task-based detectability index. Potential utility of the model was demonstrated in the optimal selection of regularization parameters in PL reconstruction. Methods: Analytical models for local modulation transfer function (MTF) and noise-power spectrum (NPS) were investigated for both FBP and PL reconstruction, including explicit dependence on the object and spatial location. For FBP, a cascaded systems analysis framework was adapted to account for nonstationarity by separately calculating fluence and system gains for each ray passing through any given voxel. For PL, the point-spread function and covariance were derived using the implicit function theorem and first-order Taylor expansion according to Fessler ["Mean and variance of implicitly defined biased estimators (such as penalized maximum likelihood): Applications to tomography," IEEE Trans. Image Process. 5(3), 493-506 (1996)]. Detectability index was calculated for a variety of simple tasks. The model for PL was used in selecting the regularization strength parameter to optimize task-based performance, with both a constant and a spatially varying regularization map. Results: Theoretical models of FBP and PL were validated in 2D simulated fan-beam data and found to yield accurate predictions of local MTF and NPS as a function of the object and the spatial location. The NPS for both FBP and PL exhibit similar anisotropic nature depending on the pathlength (and therefore, the object and spatial location within the object) traversed by each ray, with the PL NPS experiencing greater smoothing along directions with higher noise. The MTF of FBP is isotropic and independent of location to a first order approximation, whereas the MTF of PL is anisotropic in a manner complementary to the NPS. Task-based detectability demonstrates dependence on the task, object, spatial location, and smoothing parameters. A spatially varying regularization "map" designed from locally optimal regularization can improve overall detectability beyond that achievable with the commonly used constant regularization parameter. Conclusions: Analytical models for task-based FBP and PL reconstruction are predictive of nonstationary noise and resolution characteristics, providing a valuable framework for understanding and optimizing system performance in CT and CBCT.

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Section: Introductionmentioning

confidence: 99%

Task‐based detectability in CT image reconstruction by filtered backprojection and penalized likelihood estimation

et al. 2014

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“…13,14 An analytical formula for the NPS with a discrete reconstruction process was derived in Ref. 15, where the effects of sampling within the projection and angular sampling were considered. The effects of interpolation and noise aliasing caused by reconstruction pixel sampling were also studied in Ref.…”

Section: Introductionmentioning

confidence: 99%

The noise power spectrum in CT with direct fan beam reconstruction

Baek

Pelc

2010

Medical Physics

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The noise power spectrum ͑NPS͒ is a useful metric for understanding the noise content in images. To examine some unique properties of the NPS of fan beam CT, the authors derived an analytical expression for the NPS of fan beam CT and validated it with computer simulations. The nonstationary noise behavior of fan beam CT was examined by analyzing local regions and the entire field-of-view ͑FOV͒. This was performed for cases with uniform as well as nonuniform noise across the detector cells and across views. The simulated NPS from the entire FOV and local regions showed good agreement with the analytically derived NPS. The analysis shows that whereas the NPS of a large FOV in parallel beam CT ͑using a ramp filter͒ is proportional to frequency, the NPS with direct fan beam FBP reconstruction shows a high frequency roll off. Even in small regions, the fan beam NPS can show a sharp transition ͑discontinuity͒ at high frequencies. These effects are due to the variable magnification and therefore are more pronounced as the fan angle increases. For cases with nonuniform noise, the NPS can show the directional dependence and additional effects.

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“…Boedeker et al [20] and Faulkner et al [21] proposed to use the NPS and the noise equivalent quanta (NEQ) to describe the noise properties in CT images, whereas Joemai et al [7] used the NPS and variance to validate their low--dose CT model. Mieville et al [22] investigated the spatial dependency and non--stationarity of the NPS.…”

Section: Related Workmentioning

confidence: 99%

Simulation of scanner- and patient-specific low-dose CT imaging from existing CT images

et al. 2017

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Analysis of x-ray computed tomography images using the noise power spectrum and autocorrelation function

Cited by 45 publications

References 10 publications

Task‐based detectability in CT image reconstruction by filtered backprojection and penalized likelihood estimation

Task‐based detectability in CT image reconstruction by filtered backprojection and penalized likelihood estimation

The noise power spectrum in CT with direct fan beam reconstruction

Simulation of scanner- and patient-specific low-dose CT imaging from existing CT images

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