Experimental comparison of empirical material decomposition methods for spectral CT

Zimmerman, Kevin; Schmidt, Taly Gilat

doi:10.1088/0031-9155/60/8/3175

Cited by 45 publications

(52 citation statements)

References 18 publications

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“…Similar to Zimmerman et al [14], we used an ANN architecture composed of one input layer, two hidden layers, and one output layer. The input and output layers contained 24 nodes each, which correspond to 24 desired input and output energy bins (from 27 to 50 keV), respectively.…”

Section: Methodsmentioning

confidence: 99%

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A neural network-based method for spectral distortion correction in photon counting x-ray CT

et al. 2016

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Purpose Spectral CT using a photon counting x-ray detector (PCXD) shows great potential for measuring material composition based on energy dependent x-ray attenuation. Spectral CT is especially suited for imaging with K-edge contrast agents to address the otherwise limited contrast in soft tissues. We have developed a micro-CT system based on a PCXD. This system enables both 4 energy bins acquisition, as well as full-spectrum mode in which the energy thresholds of the PCXD are swept to sample the full energy spectrum for each detector element and projection angle. Measurements provided by the PCXD, however, are distorted due to undesirable physical effects in the detector and can be very noisy due to photon starvation in narrow energy bins. To address spectral distortions, we propose and demonstrate a novel artificial neural network (ANN)-based spectral distortion correction mechanism, which learns to undo the distortion in spectral CT, resulting in improved material decomposition accuracy. To address noise, post-reconstruction denoising based on bilateral filtration, which jointly enforces intensity gradient sparsity between spectral samples, is used to further improve the robustness of ANN training and material decomposition accuracy. Methods Our ANN-based distortion correction method is calibrated using 3D-printed phantoms and a model of our spectral CT system. To enable realistic simulations and validation of our method, we first modeled the spectral distortions using experimental data acquired from 109Cd and 133Ba radioactive sources measured with our PCXD. Next, we trained an ANN to learn the relationship between the distorted spectral CT projections and the ideal, distortion-free projections in a calibration step. This required knowledge of the ground truth, distortion-free spectral CT projections, which were obtained by simulating a spectral CT scan of the digital version of a 3D-printed phantom. Once the training was completed, the trained ANN was used to perform distortion correction on any subsequent scans of the same system with the same parameters. We used joint bilateral filtration (BF) to perform noise reduction by jointly enforcing intensity gradient sparsity between the reconstructed images for each energy bin. Following reconstruction and denoising, the CT data was spectrally decomposed using the photoelectric effect, Compton scattering, and a K-edge material (i.e. iodine). The ANN-based distortion correction approach was tested using both simulations and experimental data acquired in phantoms and a mouse with our PCXD-based micro-CT system for 4 bins and full-spectrum acquisition modes. The iodine detectability and decomposition accuracy were assessed using the contrast-to-noise ratio and relative error in iodine concentration estimation metrics in images with and without distortion correction. Results In simulation, the material decomposition accuracy in the reconstructed data was vastly improved following distortion correction and denoising, with 50% and 20% reductions in material conce...

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Section: Methodsmentioning

confidence: 99%

“…Various empirical methods have been proposed to compensate for PCXD spectral distortions [13, 14]. Corrections undo the distortion process, while compensation is used to offset the effect.…”

Section: Introductionmentioning

confidence: 99%

A neural network-based method for spectral distortion correction in photon counting x-ray CT

et al. 2016

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“…Beer-Lambert's transmission model states the expected number of transmitted energy-resolved photons (1) where N i is the number of detected photons and W i is the detector element sensitivity in the i th energy-bin, S(E) is the source spectrum, and µ(E, x) is the linear attenuation coefficient map of the object being imaged along a given ray path. We attempt to decompose the linear attenuation coefficient map into a specific material basis,…”

Section: Methodsmentioning

confidence: 99%

“…A two-layer feed-forward neural network was used to estimate the basis material path lengths from the post-log energy-resolved data vector, L. 1 The number of energy bins and the number of basis materials determine the number of processing elements in the input-layer and the output-layer, respectively. The number of hidden processing elements, n H , is a design parameter and was selected to minimize the mean-square-error of the estimated path lengths of the calibration step wedge phantom.…”

Section: Neural Networkmentioning

confidence: 99%

Comparison of quantitative k-edge empirical estimators using an energy-resolved photon-counting detector

Zimmerman

Schmidt

2016

SPIE Proceedings

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Using an energy-resolving photon counting detector, the amount of k-edge material in the x-ray path can be estimated using a process known as material decomposition. However, non-ideal effects within the detector make it difficult to accurately perform this decomposition. This work evaluated the k-edge material decomposition accuracy of two empirical estimators. A neural network estimator and a linearized maximum likelihood estimator with error look-up tables (A-table method) were evaluated through simulations and experiments. Each estimator was trained on system-specific calibration data rather than specific modeling of non-ideal detector effects or the x-ray source spectrum. Projections through a step-wedge calibration phantom consisting of different path lengths through PMMA, aluminum, and a k-edge material was used to train the estimators. The estimators were tested by decomposing data acquired through different path lengths of the basis materials. The estimators had similar performance in the chest phantom simulations with gadolinium. They estimated four of the five densities of gadolinium with less than 2mg/mL bias. The neural networks estimates demonstrated lower bias but higher variance than the A-table estimates in the iodine contrast agent simulations. The neural networks had an experimental variance lower than the CRLB indicating it is a biased estimator. In the experimental study, the k-edge material contribution was estimated with less than 14% bias for the neural network estimator and less than 41% bias for the A-table method.

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“…Note that I 0 is absorbed into this expansion by not normalizing the spectrum representation. The advantages of this model are: (1) as will be seen, transmission measurements can be accurately modeled at low polynomial degree d, (2) for even d the spectrum boundary conditions are satisfied if α d > 0, (3) non-negativity of the spectrum model is automatically enforced, and (4) the form of the expansion is potentially convenient for simultaneous spectrum estimation and spectral CT image reconstruction, because the expansion coefficients α n enter the transmission model in a linear combination with the material thicknesses L m . For the image reconstruction problem, the quantities L m are the projection of the unknown material maps in the spectral CT image reconstruction problem.…”

Section: Polynomial Models For Spectrum Estimationmentioning

confidence: 99%

X-ray spectrum estimation from transmission measurements by an exponential of a polynomial model

et al. 2016

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There has been much recent research effort directed toward spectral computed tomography (CT). An important step in realizing spectral CT is determining the spectral response of the scanning system so that the relation between material thicknesses and X-ray transmission intensity is known. We propose a few parameter spectrum model that can accurately model the X-ray transmission curves and has a form which is amenable to simultaneous spectral CT image reconstruction and CT system spectrum calibration. While the goal is to eventually realize the simultaneous image reconstruction/spectrum estimation algorithm, in this work we investigate the effectiveness of the model on spectrum estimation from simulated transmission measurements through known thicknesses of known materials. The simulated transmission measurements employ a typical X-ray spectrum used for CT and contain noise due to the randomness in detecting finite numbers of photons. The proposed model writes the X-ray spectrum as the exponential of a polynomial (EP) expansion. The model parameters are obtained by use of a standard software implementation of the Nelder-Mead simplex algorithm. The performance of the model is measured by the relative error between the predicted and simulated transmission curves. The estimated spectrum is also compared with the model X-ray spectrum. For reference, we also employ a polynomial (P) spectrum model and show performance relative to the proposed EP model.

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Experimental comparison of empirical material decomposition methods for spectral CT

Cited by 45 publications

References 18 publications

A neural network-based method for spectral distortion correction in photon counting x-ray CT

A neural network-based method for spectral distortion correction in photon counting x-ray CT

Comparison of quantitative k-edge empirical estimators using an energy-resolved photon-counting detector

X-ray spectrum estimation from transmission measurements by an exponential of a polynomial model

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