Full-Spectrum CT Reconstruction Using a Weighted Least Squares Algorithm With an Energy-Axis Penalty

Gonzales, Brian; Lalush, David S.

doi:10.1109/tmi.2010.2048120

Cited by 15 publications

(24 citation statements)

References 32 publications

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“…We note that the made assumptions guarantee a measurement model which is linear. This model is frequently used in the literature [24,22,42,40,30,50]. We briefly recall its known limitations.…”

Section: The Forward Problem In Multi-spectral Ctmentioning

confidence: 99%

Multi-channel Potts-based reconstruction for multi-spectral computed tomography

Kiefer¹,

Petra²,

Storath³

et al. 2021

Inverse Problems

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We consider reconstructing multi-channel images from measurements performed by photon-counting and energy-discriminating detectors in the setting of multi-spectral x-ray computed tomography (CT). Our aim is to exploit the strong structural correlation that is known to exist between the channels of multi-spectral CT images. To that end, we adopt the multi-channel Potts prior to jointly reconstruct all channels. This nonconvex prior produces piecewise constant solutions with strongly correlated channels. In particular, edges are strictly enforced to have the same spatial position across channels which is a benefit over TV-based methods whose channel-couplings are typically less strict. We consider the Potts prior in two frameworks: (a) in the context of a variational Potts model, and (b) in a Potts-superiorization approach that perturbs the iterates of a basic iterative least squares solver. We identify an alternating direction method of multipliers approach as well as a Potts-superiorized conjugate gradient method as particularly suitable. In numerical experiments, we compare the Potts prior based approaches to existing TV-type approaches on realistically simulated multi-spectral CT data and obtain improved reconstruction for compound solid bodies.

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Section: The Forward Problem In Multi-spectral Ctmentioning

confidence: 99%

Multi-channel Potts-based reconstruction for multi-spectral computed tomography

Kiefer¹,

Petra²,

Storath³

et al. 2021

Inverse Problems

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“…When E 2 − E 1 is negligable, (B.5) becomes (B.1), and (B.6) becomes (B.2). This is the Radon transfom model that has been well accepted in the CT field [48, 49]. …”

Section: Solution Of (258)mentioning

confidence: 99%

Multi-energy CT based on a prior rank, intensity and sparsity model (PRISM)

et al. 2011

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We propose a compressive sensing approach for multi-energy computed tomography (CT), namely the prior rank, intensity and sparsity model (PRISM). To further compress the multi-energy image for allowing the reconstruction with fewer CT data and less radiation dose, the PRISM models a multi-energy image as the superposition of a low-rank matrix and a sparse matrix (with row dimension in space and column dimension in energy), where the low-rank matrix corresponds to the stationary background over energy that has a low matrix rank, and the sparse matrix represents the rest of distinct spectral features that are often sparse. Distinct from previous methods, the PRISM utilizes the generalized rank, e.g., the matrix rank of tight-frame transform of a multi-energy image, which offers a way to characterize the multi-level and multi-filtered image coherence across the energy spectrum. Besides, the energy-dependent intensity information can be incorporated into the PRISM in terms of the spectral curves for base materials, with which the restoration of the multi-energy image becomes the reconstruction of the energy-independent material composition matrix. In other words, the PRISM utilizes prior knowledge on the generalized rank and sparsity of a multi-energy image, and intensity/spectral characteristics of base materials. Furthermore, we develop an accurate and fast split Bregman method for the PRISM and demonstrate the superior performance of the PRISM relative to several competing methods in simulations.

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“…By (8), we can let (13) where is the Compton scatter to primary ratio. That can be estimated by (9) and the linear attenuation coefficients, photoelectric coefficients, Compton coefficients and thickness of the aluminum step-wedge phantom. As a result (12) can be modified to give the following expression: (14) where is the measurement matrix calculated from and the scatter to primary ratio of the detector.…”

Section: X-ray Spectrum Estimationmentioning

confidence: 99%

“…One of the solutions that can be applied to polychromatic X-ray CT is the X-ray photon counting detector [6]- [9]. An X-ray tube produces photons of high flux rate and as a result energy-resolved X-ray detection is difficult when an energy-counting detector is used [7], [10].…”

Section: Introductionmentioning

confidence: 99%

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

Lee

Chen²

2015

IEEE Trans. Med. Imaging

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To improve the quantitative accuracy of linear attenuation coefficients measured by computed tomography (CT), we used a single scatter model to estimate the Compton scatter distribution and then a polychromatic image reconstruction algorithm, namely the iterative maximum-likelihood polychromatic algorithm for CT (IMPACT), was implemented to include scatter correction (SC). To perform the IMPACT, the X-ray spectra of a tube were estimated via an expectation-maximization (EM) algorithm with SC. To test the accuracy of the estimated spectra, the projection images of cubic phantoms containing different depths of polymethylmethacrylate (PMMA) were acquired. The percentage of root mean square errors (%RMSE) of the measured transmission data and calculated transmission values were used to evaluate the accuracy of the estimated spectra. In addition, a hydroxylapatite (HA) phantom was used to study streak artifacts and evaluate the accuracy of the linear attenuation coefficients estimated using the IMPACT with SC. The %RMSE of the EM-with-SC estimated spectra were all lower than 1% and were also smaller than that without SC. The error in the quantification of the HA linear attenuation was only about 3% after SC. Our results showed that the quantitative accuracy of the linear attenuation coefficients measured with a cone beam CT was improved when the IMPACT with SC was used.

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Full-Spectrum CT Reconstruction Using a Weighted Least Squares Algorithm With an Energy-Axis Penalty

Cited by 15 publications

References 32 publications

Multi-channel Potts-based reconstruction for multi-spectral computed tomography

Multi-channel Potts-based reconstruction for multi-spectral computed tomography

Multi-energy CT based on a prior rank, intensity and sparsity model (PRISM)

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

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