A Single Scatter Model for X-ray CT Energy Spectrum Estimation and Polychromatic Reconstruction

Lee, Jhih-Shian; Chen, Jyh-Cheng

doi:10.1109/tmi.2015.2395438

Cited by 14 publications

(16 citation statements)

References 39 publications

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“…For the x-ray scatter effects, one can perform scatter correction for spectrum estimation on the EM method. 27 An analogous approach can be considered to combine with the method presented in this work.…”

Section: Discussionmentioning

confidence: 99%

Estimating the spectrum in computed tomography via Kullback–Leibler divergence constrained optimization

Sidky

Barber

et al. 2018

Medical Physics

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Purpose: We study the problem of spectrum estimation from transmission data of a known phantom. The goal is to reconstruct an x-ray spectrum that can accurately model the x-ray transmission curves and reflects a realistic shape of the typical energy spectra of the CT system. Methods: Spectrum estimation is posed as an optimization problem with x-ray spectrum as unknown variables, and a Kullback-Leibler (KL) divergence constraint is employed to incorporate prior knowledge of the spectrum and enhance numerical stability of the estimation process. The formulated constrained optimization problem is convex and can be solved efficiently by use of the exponentiated-gradient (EG) algorithm. We demonstrate the effectiveness of the proposed approach on the simulated and experimental data. The comparison to the expectation-maximization (EM) method is also discussed. Results: In simulations, the proposed algorithm is seen to yield x-ray spectra that closely match the ground truth and represent the attenuation process of x-ray photons in materials, both included and not included in the estimation process. In experiments, the calculated transmission curve is in good agreement with the measured transmission curve, and the estimated spectra exhibits physically realistic looking shapes. The results further show the comparable performance between the proposed optimization-based approach and EM. Conclusions: Our formulation of a constrained optimization provides an interpretable and flexible framework for spectrum estimation. Moreover, a KL-divergence constraint can include a prior spectrum and appears to capture important features of x-ray spectrum, allowing accurate and robust estimation of x-ray spectrum in CT imaging.

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Section: Discussionmentioning

confidence: 99%

Estimating the spectrum in computed tomography via Kullback–Leibler divergence constrained optimization

Sidky

Barber

et al. 2018

Medical Physics

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“…For the conversion, mean and variance values of the reconstructed image are required to determine the conversion factors using Eq. (12). Note that the mean values correspond to the yet unknown final solution that we are seeking.…”

Section: Discussionmentioning

confidence: 99%

“…Since most CT scanners use an x-ray tube that emits an x-ray beam of a continuous spectrum, 6,12 the beam has an inherent polyenergetic nature. As a polychromatic x-ray beam passes through an object, low-energy photons are absorbed more than high-energy photons and thereby the average energy of the beam increases.…”

Section: Preliminariesmentioning

confidence: 99%

“…Most clinical CT scanners currently use a polychromatic x-ray source and energy-integrating detectors. 6,12 The ML-TR algorithm as well as the FBP algorithm, however, ignores the polyenergetic nature of the x-ray beam in the reconstruction process, and this leads to beam-hardening artifacts that degrade the CT image quality. [13][14][15][16][17][18] A way to deal with this problem is to incorporate the polychromatic nature of the x-ray source into the data acquisition model in the iterative reconstruction process.…”

Section: Introductionmentioning

confidence: 99%

“…[13][14][15][16][17][18] A way to deal with this problem is to incorporate the polychromatic nature of the x-ray source into the data acquisition model in the iterative reconstruction process. 12,18 The iterative maximum-likelihood polychromatic algorithm for CT (IMPACT) 6 models an energy-dependent linear attenuation coefficient of a voxel as a linear combination of coefficients representing the photoelectric effect and Compton scatter. Thereby, the IMPACT image has no beam hardening artifacts, in contrast with the FBP and ML-TR images.…”

Section: Introductionmentioning

confidence: 99%

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Denoising of polychromatic CT images based on their own noise properties

2016

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To effectively denoise polychromatic low-dose CT images, a novel denoising algorithm is proposed. Because this algorithm is based on the noise statistics of a reconstructed polychromatic CT image, the spatially varying noise on the image is effectively reduced so that the denoised image will have homogeneous quality over the image domain. Through a simulation and a real experiment, it is verified that the proposed algorithm can deliver considerably better performance compared to the existing denoising algorithms.

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Locally linear transform based three‐dimensional gradient ‐norm minimization for spectral CT reconstruction

Wang

Deng

et al. 2020

Medical Physics

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Purpose: Spectral computed tomography (CT) is proposed by extending the conventional CT along the energy dimension. One newly implementation is to employ an energy-discriminating photon counting detector (PCD), which can distinguish photon energy and divide a whole x-ray spectrum into several energy bins with appropriate post-processing steps. The state-of-the-art PCD-based spectral CT has superior energy resolution and material distinguishability, and it further has a great potential in both medical and industrial applications. To improve the reconstruction quality and decomposition accuracy, in this work, we propose an optimization-based spectral CT reconstruction method with an innovational sparsity constraint. Methods: We first employ a locally linear transform to the reconstructed channel images, and the structural similarity along the spectral dimension is effectively converted to a one-dimensional (1D) gradient sparsity. Then, combining the prior knowledge of piecewise constant in the spatial domain (e.g., a two-dimensional (2D) gradient sparsity feature), we unify both spectral and spatial dimensions and establish a joint three-dimensional (3D) gradient sparsity. In addition, we use the L 0-norm to measure the proposed sparsity and incorporate it as a smoothness constraint to concretize a general optimization framework. Furthermore, we develop the corresponding iterative algorithm to solve the optimization problem. Results: Both visual results and quantitative indexes of numerical simulations and phantom experiments demonstrate the proposed method outperform the conventional filtered backprojection (FBP), total variation (TV), 2D L 0-norm (L 0), and TV with low rank (TVLR)-based methods. From the image and ROI comparisons, we find the proposed method performs well in noise suppression, detail maintenance, and decomposition accuracy. However, the FBP suffers severe noise, the TV and L 0 are difficult to work consistently among different energy bins, and the TVLR fails to avoid gray value shift. The image quality assessments, such as peak signal-to-noise ratio (PSNR), normal mean absolute deviation (NMAD). and structural similarity (SSIM), also consistently indicate the proposed method can effectively removing noise and keeping fine structures in both channel-wise reconstructions and material decompositions. Conclusions: By employing a locally linear transform, the structural similarity among spectral channel images is converted to a 1D gradient sparsity and the gray value shift is effectively avoided when the difference measurement is minimized. The 3D L 0-norm jointly and uniformly measures the gradient sparsity in both spectral and spatial dimensions. The cooperation of locally linear transform and 3D L 0-norm well reinforces the global sparse features and keeps the correlation along spectral dimension without bringing gray-value distortions. The corresponding constraint optimization model is fast and stably solved by using an alternative direction technique. Both numerical simulations and phantom experi...

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A Single Scatter Model for X-ray CT Energy Spectrum Estimation and Polychromatic Reconstruction

Cited by 14 publications

References 39 publications

Estimating the spectrum in computed tomography via Kullback–Leibler divergence constrained optimization

Estimating the spectrum in computed tomography via Kullback–Leibler divergence constrained optimization

Denoising of polychromatic CT images based on their own noise properties

Locally linear transform based three‐dimensional gradient ‐norm minimization for spectral CT reconstruction

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