Generalized least-squares CT reconstruction with detector blur and correlated noise models

Stayman, J. Webster; Zbijewski, Wojciech; Tilley, Steven; Siewerdsen, Jeffrey H.

doi:10.1117/12.2043067

Cited by 7 publications

(8 citation statements)

References 9 publications

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“…We evaluate the method by comparing reconstructions using the correlated noise model with results obtained using a model that assumes spatially independent noise. This work expands upon previous work where we have shown correlated noise models are advantageous when dealing with high readout noise and no source blur (Stayman et al 2014) and in more recent work in which we introduced a regularized deblurring step (Tilley II et al 2014). The latter work considered preliminary simulation studies with three different blur scenarios using a small phantom and demonstrated that systems dominated by detector blur with low readout noise do not benefit from the proposed model, but source blur dominated systems do.…”

Section: Introductionsupporting

confidence: 54%

“…However, this assumption only holds for low readout noise. As shown in (Stayman et al 2014), a system dominated by detector blur will still benefit from a correlated noise model since deblurring will add correlations due to additive readout noise. The FDK and deblurred FDK resolution-variance points lie near the uncorrelated model's resolution-variance curve indicating similar performance.…”

Section: Simulation Studiesmentioning

confidence: 99%

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Model-based iterative reconstruction for flat-panel cone-beam CT with focal spot blur, detector blur, and correlated noise

2015

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While model-based reconstruction methods have been successfully applied to flat-panel cone-beam CT (FP-CBCT) systems, typical implementations ignore both spatial correlations in the projection data as well as system blurs due to the detector and focal spot in the x-ray source. In this work, we develop a forward model for flat-panel-based systems that includes blur and noise correlation associated with finite focal spot size and an indirect detector (e.g., scintillator). This forward model is used to develop a staged reconstruction framework where projection data are deconvolved and log-transformed, followed by a generalized least-squares reconstruction that utilizes a non-diagonal statistical weighting to account for the correlation that arises from the acquisition and data processing chain. We investigate the performance of this novel reconstruction approach in both simulated data and in CBCT test-bench data. In comparison to traditional filtered backprojection and model-based methods that ignore noise correlation, the proposed approach yields a superior noise-resolution tradeoff. For example, for a system with 0.34 mm FWHM scintillator blur and 0.70 FWHM focal spot blur, using the a correlated noise model instead of an uncorrelated noise model increased resolution by 42% (with variance matched at 6.9 × 10−8 mm−2). While this advantage holds across a wide range of systems with differing blur characteristics, the improvements are greatest for systems where source blur is larger than detector blur.

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Section: Introductionsupporting

confidence: 54%

Section: Simulation Studiesmentioning

confidence: 99%

Model-based iterative reconstruction for flat-panel cone-beam CT with focal spot blur, detector blur, and correlated noise

2015

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“…Incorporation of such complexities into model-based statistical reconstruction is an area of ongoing and future work. 49 We consider a quadratic penalty, R(μ), of the form…”

Section: C the Spatially Varying Nps And Mtf For Iterative Statistmentioning

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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“…Therefore, Eq. (2) and (3) need to be re-written for consideration of correlations when dealing with these corrections and a generalized reconstruction model as in (Stayman et al 2014, Tilley et al 2014) may be required.…”

Section: Discussionmentioning

confidence: 99%

Statistical reconstruction for cone-beam CT with a post-artifact-correction noise model: application to high-quality head imaging

et al. 2015

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Non-contrast CT reliably detects fresh blood in the brain and is the current front-line imaging modality for intracranial hemorrhage such as that occurring in acute traumatic brain injury (contrast ~40-80 HU, size > 1 mm). We are developing flat-panel detector (FPD) cone-beam CT (CBCT) to facilitate such diagnosis in a low-cost, mobile platform suitable for point-of-care deployment. Such a system may offer benefits in the ICU, urgent care/concussion clinic, ambulance, and sports and military theatres. However, current FPD-CBCT systems face significant challenges that confound low-contrast, soft-tissue imaging. Artifact correction can overcome major sources of bias in FPD-CBCT but imparts noise amplification in filtered backprojection (FBP). Model-based reconstruction improves soft-tissue image quality compared to FBP by leveraging a high-fidelity forward model and image regularization. In this work, we develop a novel penalized weighted least-squares (PWLS) image reconstruction method with a noise model that includes accurate modeling of the noise characteristics associated with the two dominant artifact corrections (scatter and beam-hardening) in CBCT and utilizes modified weights to compensate for noise amplification imparted by each correction. Experiments included real data acquired on a FPD-CBCT test-bench and an anthropomorphic head phantom emulating intra-parenchymal hemorrhage. The proposed PWLS method demonstrated superior noise-resolution tradeoffs in comparison to FBP and PWLS with conventional weights (viz., at matched 0.50 mm spatial resolution, CNR = 11.9 compared to CNR = 5.6 and CNR = 9.9, respectively) and substantially reduced image noise especially in challenging regions such as skull base. The results support the hypothesis that with high-fidelity artifact correction and statistical reconstruction using an accurate post-artifact-correction noise model, FPD-CBCT can achieve image quality allowing reliable detection of intracranial hemorrhage.

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Generalized least-squares CT reconstruction with detector blur and correlated noise models

Cited by 7 publications

References 9 publications

Model-based iterative reconstruction for flat-panel cone-beam CT with focal spot blur, detector blur, and correlated noise

Model-based iterative reconstruction for flat-panel cone-beam CT with focal spot blur, detector blur, and correlated noise

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

Statistical reconstruction for cone-beam CT with a post-artifact-correction noise model: application to high-quality head imaging

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