Characterization of energy response for photon‐counting detectors using x‐ray fluorescence

Ding, Huanjun; Cho, Hyo-Min; Barber, William C.; Iwanczyk, Jan S.; Molloi, Sabee

doi:10.1118/1.4900820

Cited by 35 publications

(26 citation statements)

References 54 publications

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“…Tabulated or computer-generated x-ray spectra are useful for computer simulations pertaining to modeling of beam shaping filter performance, 1,2 imaging performance modeling, [3][4][5][6] validation of x-ray spectral measurements, 7-9 radiation dose, 10,11 modeling of photon counting spectral/dual-energy imaging systems, 8,[12][13][14] and many other applications. Recently, a tungsten anode spectral model using interpolating cubic splines (TASMICS 15 ) was proposed to update the previous tungsten anode spectral model using interpolating polynomials (TASMIP 16 ).…”

Section: Introductionmentioning

confidence: 99%

Generation and analysis of clinically relevant breast imaging x-ray spectra

et al. 2017

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Purpose The purpose of this work was to develop and make available x-ray spectra for some of the most widely used digital mammography (DM), breast tomosynthesis (BT), and breast CT (bCT) systems in North America. Methods The Monte Carlo code MCNP6 was used to simulate minimally-filtered (only beryllium) x-ray spectra at 8 tube potentials from 20 to 49 kV for DM/BT, and 9 tube potentials from 35 to 70 kV for bCT. Vendor-specific anode compositions, effective anode angles, focal spot sizes, source-to-detector distances, and beryllium filtration were simulated. For each 0.5 keV energy bin in all simulated spectra, the fluence was interpolated using cubic splines across the range of simulated tube potentials to produce spectra in 1 kV increments from 20 to 49 kV for DM/BT and from 35 to 70 kV for bCT. The HVL of simulated spectra with conventional filtration (at 35 kV for DM/BT and 49 kV for bCT) was used to assess spectral differences resulting from variations in: (1) focal spot size (0.1 and 0.3 mm IEC), (2) solid angle at the detector (i.e. small and large FOV size), and (3) geometrical specifications for vendors that employ the same anode composition. Results Averaged across all DM/BT vendors, variations in focal spot and FOV size resulted in HVL differences of 2.2% and 0.9%, respectively. Comparing anode compositions separately, the HVL differences for Mo (GE, Siemens) and W (Hologic, Philips, and Siemens) spectra were 0.3% and 0.6%, respectively. Both the commercial Koning and prototype “Doheny” (UC Davis) bCT systems utilize W anodes with a 0.3 mm focal spot. Averaged across both bCT systems, variations in FOV size resulted in a 2.2% difference in HVL. In addition, the Koning spectrum was slightly harder than Doheny with a 4.2% difference in HVL. Therefore to reduce redundancy, a generic DM/BT system and a generic bCT system were used to generate the new spectra reported herein. The spectral models for application to DM/BT were dubbed the Molybdenum, Rhodium, and Tungsten Anode Spectral Models using Interpolating Cubic Splines (MASMICSM-T, RASMICSM-T, and TASMICSM-T ; subscript “M-T” indicating mammography and tomosynthesis). When compared against reference models (MASMIPM, RASMIPM, and TASMIPM; subscript “M” indicating mammography), the new spectral models were in close agreement with mean differences of 1.3%, −1.3%, and −3.3%, respectively, across tube potential comparisons of 20, 30, and 40 kV with conventional filtration. TASMICSbCT-generated bCT spectra were also in close agreement with the reference TASMIP model with a mean difference of −0.8%, across tube potential comparisons of 35, 49, and 70 kV with 1.5 mm Al filtration. Conclusions The Mo, Rh, and W anode spectra for application in DM and BT (MASMICSM-T, RASMICSM-T, and TASMICSM-T) and the W anode spectra for bCT (TASMICSbCT) as described in this study should be useful for individuals interested in modeling the performance of modern breast x-ray imaging systems including dual energy mammography which extends to 49 kV. These new spectra are t...

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Section: Introductionmentioning

confidence: 99%

Generation and analysis of clinically relevant breast imaging x-ray spectra

et al. 2017

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“…Here the analytic detector response function [27] was utilized to simulate the non-ideal detector response. With properly selected energy intervals, the raw spectral data with non-ideal detector response were corrected to the spectral data for ideal detector response so that the proposed TICMR method can be applied directly based on the model (4) with ideal detector response.…”

Section: Resultsmentioning

confidence: 99%

“…Here the R matrix is defined as

R_{n l} = \int_{normalΔ E_{l}^{'}} d E' \int_{normalΔ E_{n}} D false(E', E false) S false(E false) d E .

where the detector response function D ( E ′, E ) is calibrated using X-ray fluorescence [27], and then the Poisson noise was added to the measurements pointwisely, i.e.,

Y_{l} = Poisson false(Y_{l}^{*} false), for l = 10, \dots, 65 .

Finally, with a proper choice of energy intervals, the interval 10 ≤ Ẽ ≤ 65 was divided into five energy groups 10 ≤ E 1 ≤ 32, 33 ≤ E 2 ≤ 39, 40 ≤ E 3 ≤ 47, 48 ≤ E 4 ≤ 57, 58 ≤ E 5 ≤ 65, and then corrected projection data and total projection data were as follows,

\bar{P} = - log \frac{\sum_{l = 1}^{65} Y_{l}}{\sum_{l = 1}^{65} \sum_{n = 1}^{65} R_{n l}};

and

\tilde{P} = - log false(Ỹ {\tilde{R}}^{- 1} false) .

where

Ỹ_{m} = \sum_{l \in E_{m}} Y_{l}

, for 1 ≤ m ≤ 5,

{\tilde{R}}_{m k} = \sum_{l \in E_{m}} \sum_{n \in E_{k}} R_{n l}

, for 1 ≤ m, k ≤ 5.…”

Section: Resultsmentioning

confidence: 99%

“…Let M = N · N e be the total number of spectral data, s ( E ) the incident spectrum, Δ E m the length of the m th energy interval, and L i the path of line integral for Y im . Assuming the perfect detector response [27], the expectation

Y_{i m}^{*}

of spectral measurement Y im is given by the following spectral model for i = 1, …, N and m = 1, …, N e

Y_{i m}^{*} = \int_{normalΔ E_{m}} s false(E false) e^{- \int_{L_{i}} u false(x, E false) d x} d E

where multi-energy attenuation coefficient u ( x, E ) linearly depends on the material composition Z [7], i.e.,

u false(x, E false) = \sum_{k = 1}^{N_{z}} Z_{k} false(x false) B_{k} false(E false) .

Here N z is the number of basis materials, Z k ( x ) is the material composition of the k th basis material at the spatial location x , which is spectrally independent, and B k ( E ) is the attenuation coefficient of the k th basis material at the energy E , which is spatially independent. For example, the incident spectrum s ( E ) with 65KeV tube voltage and B ( E ) for several materials are plotted in Fig.…”

Section: Methodsmentioning

confidence: 99%

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TICMR: Total Image Constrained Material Reconstruction via Nonlocal Total Variation Regularization for Spectral CT

Liu

Ding

Molloi

et al. 2016

IEEE Trans. Med. Imaging

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This work develops a material reconstruction method for spectral CT, namely Total Image Constrained Material Reconstruction (TICMR), to maximize the utility of projection data in terms of both spectral information and high signal-to-noise ratio (SNR). This is motivated by the following fact: when viewed as a spectrally-integrated measurement, the projection data can be used to reconstruct a total image without spectral information, which however has a relatively high SNR; when viewed as a spectrally-resolved measurement, the projection data can be utilized to reconstruct the material composition, which however has a relatively low SNR. The material reconstruction synergizes material decomposition and image reconstruction, i.e., the direct reconstruction of material compositions instead of a two-step procedure that first reconstructs images and then decomposes images. For material reconstruction with high SNR, we propose TICMR with nonlocal total variation (NLTV) regularization. That is, first we reconstruct a total image using spectrally-integrated measurement without spectral binning, and build the NLTV weights from this image that characterize nonlocal image features; then the NLTV weights are incorporated into a NLTV-based iterative material reconstruction scheme using spectrally-binned projection data, so that these weights serve as a high-SNR reference to regularize material reconstruction. Note that the nonlocal property of NLTV is essential for material reconstruction, since material compositions may have significant local intensity variations although their structural information is often similar. In terms of solution algorithm, TICMR is formulated as an iterative reconstruction method with the NLTV regularization, in which the nonlocal divergence is utilized based on the adjoint relationship. The alternating direction method of multipliers is developed to solve this sparsity optimization problem. The proposed TICMR method was validated using both simulated and experimental data. In comparison with FBP and total-variation-based iterative method, TICMR had improved image quality, e.g., contrast-to-noise ratio and spatial resolution.

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“…A method for establishing the energy response function of Si-strip photon counting detectors used for XRF-CT was reported by Ding et al 94 who used a tungsten target X-ray tube operated at 80 kV, various beam lters and samples containing Ag, Ba, Gd or I. A mathematical model for the response function of a Si(PIN) detector was proposed 92 in which there were four components: a Gaussian peak; a truncated shelf; an exponential tail and a Gaussian silicon escape peak.…”

Section: X-ray Detectorsmentioning

confidence: 99%