Signal detection and location‐dependent noise in cone‐beam computed tomography using the spatial definition of the Hotelling SNR

Brunner, Claudia C.; Abboud, Samir F.; Hoeschen, Christoph; Kyprianou, Iacovos S.

doi:10.1118/1.4718572

Cited by 21 publications

(39 citation statements)

References 25 publications

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“…12 Empirical determination of the full covariance matrix requires a large number of noisy realizations to achieve reasonable accuracy. As a rule of thumb, 5,6 the number of reconstructions required is at least 10 times the number of samples, i.e., 10 × n 2 . This is challenging even in simulated data, although efforts have been made to improve estimation accuracy using fewer data sets with assumptions on the correlation length in linear reconstruction algorithms (e.g., FBP).…”

Section: E Analysis Of Noise and Spatial Resolutionmentioning

confidence: 99%

“…where S proj denotes the 2D projection NPS, Conversion gain from x-rays to secondary quanta (e.g., optical photons) P k Gain and spreading factors associated with K-fluorescence T 3 Transfer function due to stochastic spread of secondary quantā g 4 Coupling efficiency of photodiode a pd Width of (square) photodiode T 5 Transfer function due to photodiode aperture III 6 Detector pixel sampling (2D comb function) σ add Additive electronics noise III 8 Postreadout projection resampling (optional) T 8 Transfer function due to 2D binning aperture (optional) T 10 Ramp filter T 11 Apodization filter T 12 Interpolation filter T 13 Transfer function associated with backprojection of signal 13 Transfer function associated with backprojection of noise III 14 3D voxel sampling (3D comb function) III 15 Postreconstruction sampling (optional) T 15 Transfer function due to 3D binning aperture (optional) m Number of projections acquired across a circular orbit θ tot Total angular extent of acquisition M Magnification factor, source-detector distance (SDD)/source-axis distance (SAD) FOV Size of the reconstruction field of view…”

Section: B the Spatially-varying Nps And Mtf For Fbpmentioning

confidence: 99%

“…5 The local NPS and MTF can then be related to task-based imaging performance via Eqs. (11) and (12).…”

Section: -6mentioning

confidence: 99%

“…Bartolac et al 15 investigated the nonstationary signal and noise characteristics in CBCT arising specifically from sampling along a circular source-detector trajectory (i.e., the spatially varying null cone associated with violation of Tuy's condition). Nonstationarity in relation to task-based performance was investigated by Brunner et al, 5 who evaluated the location-dependent NPS and covariance matrix in FBP reconstructions and calculated Hotelling observer performance for simple tasks. Wunderlich and Noo 16 estimated the covariance in FBP reconstruction of fan-beam CT data and examined the location-dependent noise and lesion detectability using a channelized Hotelling observer.…”

Section: Introductionmentioning

confidence: 99%

“…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%

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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: E Analysis Of Noise and Spatial Resolutionmentioning

confidence: 99%

Section: B the Spatially-varying Nps And Mtf For Fbpmentioning

confidence: 99%

“…5 The local NPS and MTF can then be related to task-based imaging performance via Eqs. (11) and (12).…”

Section: -6mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2014

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Pixel-wise estimation of noise statistics on iterative CT reconstruction from a single scan

Wang

Zhu

2017

Med. Phys.

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Purpose As iterative CT reconstruction continues to advance, the spatial distribution of noise standard deviation (STD) and accurate noise power spectrum (NPS) on the reconstructed CT images become important for method evaluation as well as optimization of algorithm parameters. Using a single CT scan, we propose a practical method for pixel‐wise calculation of noise statistics on an iteratively reconstructed CT image, which enables accurate calculation of noise STD for each pixel and NPS. Method We first derive the noise propagation from measured projections to an iteratively reconstructed CT image provided that the projection noise is known. We then show that the model of noise propagation remains approximately unchanged for extra simulated noise added on the measured projections. To compute the noise STD map and the NPS map on an iteratively reconstructed CT image from a single scan, we first iteratively reconstruct the CT image from the measured projections using an existing reconstruction algorithm. The same measured projections are added by different sets (a total of 32 sets in our implementation) of projection noise simulated from an estimated projection noise model, and are then used to iteratively reconstruct different CT images. The calculations of the noise STD map and the NPS map are finally performed on the entire stack of these different reconstruction images. Results We evaluate our method on an anthropomorphic head phantom, and demonstrate the clinical utility on a set of head and neck patient CT data, using two iterative CT reconstruction algorithms: the penalized weighted least‐square (PWLS) algorithm and the total‐variation (TV) regularization. In the head phantom case, repeated scans are acquired to generate the ground truths of noise STD and NPS maps. Using only one single scan, the proposed method accurately calculates the noise STD maps with a root‐mean‐square error (RMSE) of less than 5HU. In the NPS map estimation, we compare the result of our proposed method with that of the conventional method which calculates the NPS maps on a uniform region of interest on one CT image. Our method outperforms the conventional method on the NPS map estimation with RMSE reduced by 92%. The implementation of the proposed method on the patient data successfully provides the noise STD values around complex structures and a high‐quality NPS map. Conclusion The proposed method accurately calculates noise STD for each pixel and NPS on an iteratively reconstructed CT image, with no requirement of repeated CT scans. It provides a detailed evaluation of imaging performance of different iterative reconstruction methods on the same CT dataset.

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A method for characterizing and matching CT image quality across CT scanners from different manufacturers

2017

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Signal detection and location‐dependent noise in cone‐beam computed tomography using the spatial definition of the Hotelling SNR

Abstract: By using the eigenvectors of the noise and object transfer to characterize the system, the spatial approach provides additional information to the Fourier approach and is therefore an important tool for a thorough understanding of a CT system.

Cited by 21 publications

References 25 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

Pixel-wise estimation of noise statistics on iterative CT reconstruction from a single scan

A method for characterizing and matching CT image quality across CT scanners from different manufacturers

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