A photon-counting detector for dual-energy breast tomosynthesis
Erik Fredenberg, Mats Lundqvist, Magnus Aslund, Magnus Hemmendorff, Bjorn Cederstrom, Mats Danielsson
This is the submitted manuscript of:
Fredenberg, E., Lundqvist, M., Åslund, M., Hemmendorff, M., Cederström, B. and Danielsson, M., “A photon -counting detector for dual- energy breast tomosynthesis,” Proc. SPIE 7258, Medical
Imaging 2009: Physics of Medical Imaging, 72581J (2009).
The published version of the manuscript is available at: https://doi.org/10.1117/12.813037 See also:
Berggren, K., Cederström, B., Lundqvist, M. and Fredenberg, E., 2018. Characterization of photon‐ counting multislit breast tomosynthesis. Medical physics, 45(2), pp.549-560. https://doi.org/10.1002/mp.12684 All publications by Erik Fredenberg: https://scholar.google.com/citations?hl=en&user=5tUe2P0AAAAJ photon-counting detector for dual-energy breasttomosynthesis
Erik Fredenberg, a Mats Lundqvist, b Magnus ˚Aslund, b Magnus Hemmendorff, b Bj¨ornCederstr¨om, a and Mats Danielsson aa Department of Physics, Royal Institute of Technology (KTH), AlbaNova University Center,SE-106 91 Stockholm, Sweden b Sectra Mamea AB, Smidesv¨agen 5, SE-171 41 Solna, Sweden;
ABSTRACT
We present the first evaluation of a recently developed silicon-strip detector for photon-counting dual-energybreast tomosynthesis. The detector is well suited for tomosynthesis with high dose efficiency and intrinsic scatterrejection. A method was developed for measuring the spatial resolution of a system based on the detector in termsof the three-dimensional modulation transfer function (MTF). The measurements agreed well with theoreticalexpectations, and it was seen that depth resolution was won at the cost of a slightly decreased lateral resolution.This may be a justifiable trade-off as clinical images acquired with the system indicate improved conspicuity ofbreast lesions. The photon-counting detector enables dual-energy subtraction imaging with electronic spectrum-splitting. This improved the detectability of iodine in phantom measurements, and the detector was found to bestable over typical clinical acquisition times. A model of the energy resolution showed that further improvementsare within reach by optimization of the detector.
Keywords: tomosynthesis; spatial resolution; dual-energy subtraction; energy resolution; photon counting;mammography;
1. INTRODUCTION
Breast tomosynthesis and contrast-enhanced dual-energy subtraction (DES) imaging, are two promisingmethods to improve the conspicuity of breast lesions in mammography, offering an alternative to MRI. A photon-counting scanned multi-slit mammography system with an array of silicon-strip detectors has recently beenadapted for breast tomosynthesis within the EU-funded HighReX-project. Clinical trials have begun during thefall.The HighReX system is particularly well suited for tomosynthesis for at least two reasons. (1) Multi-slitgeometries provide intrinsic and efficient scatter rejection. This is contrary to systems that rely on Buckygrids, which are relatively inefficient for mammography energies and hard to integrate in tomosynthesis. Scatterrejection is important in tomosynthesis, in particular for large and dense breasts where tomosynthesis is expectedto be most beneficial because of the reduced conspicuity of lesions. (2) Compared to energy-integration, photoncounting provides improved energy weighting, and it is possible to eliminate virtually all electronic noise. The result is higher dose efficiency, which is important in tomosynthesis since the dose in each projection mustbe kept low.Moreover, photon counting allows the energy of individual photons to be measured. The silicon-strip de-tector that is used in the described tomosynthesis system is able to separate impinging photons into two binsaccording to their energy. One application of such energy sensitivity is contrast-enhanced DES imaging usingelectronic spectrum-splitting, which is more efficient than dual-spectra methods because of reduced motion arti-facts and narrower spectra.
6, 7
The detector is also equipped with anti-coincidence logic to reduce the effects ofcharge sharing between adjacent strips and improve the energy resolution.We present an evaluation of the HighReX system, divided into two parts; tomosynthesis and DES imaging.Tomosynthesis was studied on a system level in a prototype. Clinical images have been acquired, and the system
Electronic mail: [email protected] as characterized in terms of the resolution. DES is not yet implemented on this first system, and energysensitivity was examined on a detector level using a single detector line. We demonstrate a model of the energycharacteristics of the detector, which is based on theoretical considerations and measurements.
2. MATERIAL AND METHODS2.1. Background
Tomosynthesis allows for three-dimensional reconstruction from a set of limited-angle projections. Throughoutthe study, the x - y -plane refers to the lateral directions in the object, with detector strips in the x -direction andtube motion and scanning along y . The z -axis is the depth direction. ν x , ν y , and ν z are the respective spatialfrequencies.Tomosynthesis reconstruction can be approximately described with the Fourier-slice theorem, stating thatthe Fourier transform of a projection line is equal to a slice at the same angle through the origin of the two-dimensional (2D) Fourier transform of the reconstructed plane. As opposed to computed tomography with afull angular coverage, tomosynthesis restrains the Fourier domain of the reconstructed plane to a sheaf-shapedarea around the origin. One implication of the restricted Fourier plane is a limited z -resolution, in particular forlow ν y , which show up as shadows that transfer through the planes. Another implication is an edge enhancementin y .There is not yet a standardized method of measuring tomosynthesis resolution. The y -resolution may bemeasured separately from z with standard methods, but the results can be misleading since the influence ofout-of-plane structures is not taken into account. Instead, we make an attempt to estimate the 2D modulationtransfer function (MTF) in the y - z -plane, based on a measurement of the 2D point-spread function (PSF). In x , the resolution is virtually unaffected by the reconstruction process and determined by the source size and thedetector. Being independent of y and z , the x -MTF can be calculated from a measurement of the one-dimensional(1D) line-spread function. DES imaging with electronic spectrum-splitting as used in the HighReX system has been described in detailpreviously,
6, 7 but is reviewed here for clarity. An x-ray detector with an energy threshold makes it possible tosimultaneously record high- and low-energy images ( n hi and n lo ) by sorting registered photons into two bins.By logarithmically subtracting the two images with a proper weighting factor ( w ) the contrast between any twomaterials (e.g. glandular and adipose tissue) in the object can be made to cancel, whereas other materials arestill visible. The effect is largest if the spectrum is split at an absorption edge of a contrast agent material. TheDES signal ( I DES ) and signal difference (∆ I DES ) are thus formed; I DES = ln n hi − w ln n lo and ∆ I DES = (cid:175)(cid:175) I − I (cid:175)(cid:175) . (1)It has been shown that ∆ I DES is independent of exposure. w is chosen so as to minimize the noise from the anatomical background, which is calculated as the standarddeviation of I DES measured with negligible quantum noise over a range of glandular fractions, g i ; σ w ( w ) = (cid:195) m − m (cid:88) i (cid:104) I DES ( g i , w ) − I DES ( w ) (cid:105) (cid:33) / , (2)where I DES ( w ) is the mean over all glandular fractions. Note that w is also exposure-independent. .2. Description of the system and experimental set-up The HighReX tomosynthesis system is a modification of the Sectra MicroDose Mammography (MDM) sys-tem.
9, 13
The MDM system is a scanning multi-slit full-field digital mammography system, which comprises amammography x-ray tube, a pre-collimator, and an image receptor, all mounted on a common arm (Fig. 1, left).To acquire an image, the arm is rotated around the center of the source so that the detector and pre-collimatorare scanned across the object. In the HighReX system, however, the center of rotation is shifted to a pointbelow the detector so that the source movement describes an arc above the object, while the detector and pre-collimator scan the object. Hence, each point in the object is viewed from a range of source-detector angles bydifferent detector segments as the detector scans the object. The angular coverage is limited by the width ofthe detector to 11 ◦ . This scheme is different from tomosynthesis with flat-panel detectors as two-dimensionalprojection images are not acquired successively, but the reconstruction principle is equal. The advantages includemore efficient scatter rejection and less focal spot blurring as the detector moves with the source. Figure 1, rightshows a photograph of the HighReX system. The source and beam quality are similar to the MDM system.The image reconstruction is based on the convex algorithm introduced for transmission imaging by Lange. It is an iterative method, similar to expectation maximization, with the calculation of a likelihood functionby forward projection, and maximization of the function by Newton’s method. Iterative methods have provenefficient for limited data reconstructions, and the intense calculations are no longer considered a problem. Allimages in this study have been reconstructed with a 3 mm slice thickness and without any filtering post processing. pre- collimator breast x-ray tube detector yz x breast x-ray beam Si-strip detector lines pre- collimator compression plate breast support _ + HV rejection high low detector line ASIC 1010101 1010101 AC
Figure 1. Left:
In the MDM system, the arm is rotated around the center of the source to acquire a 2D image. In theHighReX system the center of rotation is shifted to a point below the detector so that the source movement describes anarc above the object. Each point in the object is hence viewed from a range of source-detector angles.
Middle:
A closeup of the image receptor and the electronics.
Right:
A photo of the prototype HighReX system.
The image receptor in the HighReX system consists of silicon-strip detectors with a strip-pitch of 50 µ m, arrangededge-on for high quantum efficiency despite the low atomic number of silicon (Fig. 1, middle). There are 21detector lines, which determine the number of projections in the tomosynthesis acquisitions. For each line, thereis a corresponding collimator slit in the pre-breast collimator. bias voltage is applied over the strip detector (Fig. 1, middle). When a photon interacts with the detectormaterial by the photoelectric effect, charge is released and drifts as electron-hole pairs towards the anode andcathode respectively. Each strip is wire bonded to a preamplifier and shaper, which collect the charge and convertit to a pulse. The pulse height is proportional to the charge and thus to the energy of the impinging photon.Pulses below a certain threshold are regarded as noise and are rejected by a discriminator. All remaining pulsesare registered by a counter. A preamplifier with discriminator and counter is referred to as a channel, and allchannels are implemented in an application specific integrated circuit (ASIC). Similar detectors and electronicsare in use in the Sectra MDM system.
11, 12, 15
A new feature of the present ASIC is an additional higher threshold of the discriminator with a correspondingadditional counter, which is used to sort the detected pulses into two bins according to energy, and thus to allowfor DES imaging as described above.A second novelty is anti-coincidence (AC) logic to remedy the effects of charge sharing. Charge sharingoccurs when a photon is absorbed close to the border between two strips and the charge is split between thecorresponding channels. Without AC, two photons of lower energy would be detected instead of one high-energyphoton, which would increase the noise since the shared photon is double counted (counted twice). Chargesharing would also degrade the spatial resolution since the signal is blurred between two pixels, and the energyresolution since the energy is divided into two parts. The AC logic distinguishes charge-shared events by asimultaneous detection in two adjacent channels, and the event is registered only once in the high-energy binof the channel with the largest signal. Note that the shared charge needs to be large enough to reach over thelow-energy threshold in order to be detected.
As noted above, DES is not yet implemented in the HighReX system, and measurements were therefore performedwith a single 128-channel detector element in a set-up similar to a 2D scanned-slit mammography geometry. Theeffective source size was 400 × µ m, and the beam was filtered with aluminum absorption filters. A collimatorslit up-stream of the object matched the detector, and the object was scanned across the beam to acquire animage. The lower threshold of the detector was set to discriminate against pulses below approximately 13 keV,and the higher threshold to split the spectrum at approximately 33 keV, corresponding to the K-edge of iodine.To measure the energy spectrum, a CZT compound solid state detector ∗ was inserted in the beam path. It hasa near 100% detection efficiency and negligible hole tailing in the considered energy interval.DES measurements in the same set-up have been presented in a previous study, and here we evaluate someof the results further. A phantom was used, consisting of a PMMA slab with 1-9 mm deep containers filled withiodinated contrast agent. † The iodine was diluted, and the concentration was measured by x-ray absorption to3.75 mg/ml, which is a realistic concentration for tumor uptake. To hide the iodine containers, the slab wascovered with antropomorphic clutter made of olive oil and PMMA. These constituents correspond in absorptiondifference approximately to adipose and fibroglandular tissue, and the anatomical noise was shown to correspondfairly well with real breast tissue. The total thickness of the phantom was 4.5 cm. A wedge with PMMA-to-oilfractions ranging from 10% to 90% was used to simulate a variety of glandularities for determination of w . Theaverage glandular dose (AGD) was calculated by applying normalized glandular dose coefficients to a measuredspectrum. Clinical trials were performed with the HighReX system during the fall of 2008 at Capio/St. G¨oran’s Hospitalin Stockholm, Sweden. Samples of the acquired images are shown in this study.To measure the PSF in the y - z -plane, we used a 50 µ m thin tungsten wire slanted in the plane at 12.3 ◦ to the y -axis. The 2D PSF, which is pre-sampled in z but not in y , was calculated from a single slice in thereconstructed volume with the wire angle as input.
3, 18
The in-plane PSF in y was measured at the waist of ∗ Amptek XR-100T-CZT † Ultravist 370, BayerSchering, Germany he 2D PSF. As noted above, this measurement may give misleading results, but it was nevertheless includedto facilitate comparisons to other studies. The in-plane PSF in the x -direction is on the contrary a meaningfulquantity as it is virtually independent of the y - z -resolution. It was measured with the same wire, but slanted inthe x - y -plane for over-sampling. The measurement was somewhat complicated by the strong edge enhancementin the y -direction; the wire is erroneously enhanced by its’ y -component. We overcame this problem by using avery slight angle and over sample at well separated points on the wire. From the 1D and 2D PSF’s, the MTF’swere calculated with 1D and 2D fast Fourier transforms. The purpose of the DES measurements was to fully understand previous experimental results, and to provideinput to a model of the detector energy sensitivity.Firstly, the stability of the energy thresholds over time was quantified by recording the high- and low-energy count rates in a flat-field image during a long period of time. Threshold fluctuations have been observedpreviously, and it is important to verify that the time scale is larger than a typical acquisition time of 10 s.Secondly, the linearity of the detector was measured as the count rate at an increasing photon-absorptionrate. By fitting the function r = R · exp( − Rτ ) to the recorded count rate, the dead time τ can be calculated. R is the photon rate, which was extrapolated from the linear curve through points at very low count rates. Alinearity measurement is important when considering energy resolution in order to avoid pile-up. At count ratesthat are approaching 1 /τ , two or more photons may hit the same detector element within one read out, and asingle high-energy photon is recorded instead of several photons of lower energy.Thirdly, the detector model was set up using the MATLAB software package. ‡ Four different effects weretaken into account; quantum efficiency, intrinsic energy resolution of silicon, charge sharing and the AC logic,and the spread in threshold levels between different channels.Quantum efficiency was calculated with published linear absorption coefficients as input. The 500 µ m thicksilicon wafer was arranged at an angle of 4 ◦ , which yields an effective detector thickness of 7.2 mm. Photo-electricevents were detected, whereas scattered events only filtered the beam and no secondary interactions of scatteredphotons were considered.The intrinsic energy resolution due to a low number of released charge pairs was modeled as normal distributedwith standard deviation σ = √ Eη(cid:178) , where E is the photon energy, (cid:178) = 3 .
66 eV is the energy needed to createan electron hole pair in silicon, and η = 0 .
115 is the Fano factor for silicon. Charge-sharing data for a similar detector was used to calculate the fraction of events that share enoughenergy with the adjacent strip to reach over the low-energy threshold and trigger the AC logic, and the decline inenergy of those that do not. We do, however, anticipate some leakage in the logic, i.e. charge-shared events thatare not caught by the logic and therefore double counted. Leakage correlates the pixel noise and can therefore beseen as a bent noise power spectrum (NPS) in the detector direction. To estimate the leakage, M = 512 128 × ν x = ν x = 0 (NPS(0)) is the variance of the total integrated pixelvalues between all ROI’s, but it is somewhat larger if there is leakage. The fraction double-counted photons ( χ )and the fractional leakage ( ξ ) can therefore be calculated according to χ = NPS(0) − L − H L + H ) − NPS(0) and ξ = NPS(0) − L − H NPS(0) − L + H , (3)where L and H are the average signals in the low- and high-energy bins respectively. A detailed description ofthe procedure can be found elsewhere. A spectrum measured with the CZT spectrometer was processed in a model with the three described detectoreffects. The energy levels of individual channel thresholds were then determined by comparing the measuredrelative count rate in the high- and low-energy bins with the model. The spread in threshold levels was assumedto be normal distributed, and the standard deviation was calculated. ‡ The MathWorks Inc., Natick, Massachusetts . RESULTS3.1. Tomosynthesis
Figure 2 shows two different slices from a tomosynthesis breast image acquired during clinical trials with theHighReX system. A group of micro calcifications is clearly seen (left), and a cyst is found further down in thebreast (right). These images serve to illustrate the capabilities of the system.
Figure 2.
Two slices from a tomosynthesis breast image acquired during clinical trials with the HighReX system.
Left:
A group of micro calcifications.
Right:
A cyst is found further down in the breast. Image courtesy of the HighReXproject.
Figure 3 shows the in-plane PSF’s in x and y with full-widths-at-half-maximum (FWHM’s) of 51 and 178 µ mrespectively. The dips around the y -peak correspond to edge-enhancement. In Fig. 4, the in-plane MTF’s areshown together with previously presented results for the MDM system. The agreement is almost perfect in x , which is expected, and any discrepancies are easily covered by differences in the measuring methods. In y ,the tomosynthesis resolution is slightly worse than the projection measurement, but there is edge enhancement,which is visible as a bump around ν y = 1 mm − . i n t en s i t y PSF yPSF x
Figure 3.
The in-plane PSF in x and y . ν or ν [mm −1 ] i n − p l a n e M T F MDM yHighReX y
MDM xHighReX xyx
Figure 4.
The in-plane MTF in x and y compared topublished results for the MDM system. As was described above, the in-plane resolution in y is of limited interest as it does not take the complete PSFinto account. Instead, Fig. 5 shows the 2D y - z PSF along with the cross section in z . The (FWHM) is 2.7 mm,which indicates high anisotropy compared to y , and the long tails forecast poor low-frequency resolution. Figure 6shows the 2D MTF in ν y and ν z , along with projections at low and medium frequencies in both directions. The y -resolution at low ν z is slightly worse than the in-plane resolution, and the suppression of low ν y grows strongerat higher ν z . In z , the MTF at low ν y drops quickly, and everything above approximately 0.05 mm − can beregarded aliasing. At higher ν y , the z -resolution extends 2-4 times longer. −2 0 2−15−10−5051015 −20−1001020 z [ mm ] intensity -2 0 2y [mm] Figure 5.
The 2D PSF in y and z , with the intensitydistribution along the z axis. ν y [mm −1 ] ν z [ mm − ] MTF=1 MTF=0.3MTF=0.1MTF=0.5
Figure 6.
The 2D MTF in y and z . Figure 8, shows an absorption image of the oil/PMMA phantom at an AGD of 0.5 mGy, and the DES imagecalculated with w = 0 .
72. None of the containers is distinguishable in the absorption image, whereas at leastfive are visible in the subtracted image. ν y [mm −1 ] M TF ν z = 0 mm −1 ν z = 0.05 mm −1 ν z [mm −1 ] M TF ν y = 0.23 mm −1 ν y = 2 mm −1 Figure 7.
Projections of the 2D MTF along the ν y -axis (left), and ν z -axis (right). [mm] [ mm ] [mm] [ mm ] Figure 8. Left:
An absorption image of the anatomical clutter phantom with 1-9 mm iodine containers.
Right:
Thecorresponding DES image calculated with w = 0 . . The five deepest holes are visible.
The DES image in Fig. 8 exhibits contrast variations over the approximately two-hour acquisition. Such vari-ations are further illustrated in Fig. 9, where a long-term decline of 0.36% per hour is seen along with short-termfluctuations. All variations are likely due to a drifting high-energy threshold, since the DES signal is independentof tube output and the absorption signal, also shown in the figure, is virtually constant. The statistical errorsof the measurements were comparably small. During the typical time scale of a clinical acquisition (10 s) themaximum variation in the DES signal is 0.30%, which is negligible for most purposes.Figure 10 shows the photon rate and detected count rate as a function of x-ray tube current times the exposeddetector width. The dead time was calculated to τ = 247 ns, corresponding to a read-out rate of 4.05 MHz.For all measurements presented here, the count-rate was approximately 30 kHz, thus more than an order ofmagnitude lower, and pile-up should be negligible.The NPS was measured and used to find the fractional leakage, ξ = 13%, and the fraction double-countedphotons, χ = 1 .
20 40 60 80 100 120−0.4−0.200.20.40.6 time [minutes] s i gna l d i ff e r en c e f r o m m ean [ % ] subtraction signalabsorption signal Figure 9.
Stability of the detector over time. The ab-sorption signal is virtually constant, whereas the DESsignal exhibits fluctuations. × mm r a t e [ k H z ] photon ratemeasured countsfitted counts Figure 10.
The linearity of the detector. The declinein detected count rate due to pile-up at higher photonrates is clearly seen. detectors. The mean of the energy thresholds was determined to 30 keV with a standard deviation of ± . I DES ) for the PMMA/oil phantom comparedto measured values. Large fluctuations in the measured ∆ I DES are seen, which should again be due to timevariations since the statistical errors are small. A least-square fit of the measurements (with the signal at 9 mmconsidered an outlier), however, is in almost perfect agreement with the model prediction for the experimentaldetector. The model predicts that an optimized detector with no threshold spread, a split frequency of 33 keV,and perfect AC logic that discards charge-shared photons instead of directing them to the high-energy bin,enables an improvement in I DES of 38%.
26 27 28 29 30 31 32 330510152025 energy [keV] nu m be r o f c hanne l s Figure 11.
The spread of the high-energy thresh-olds. The mean is 30 keV with a standard deviation of ± . ∆ I experimental detector optimized detectormeasurementsmodel: D E S Figure 12.
The DES signal difference (∆ I DES ) as afunction of depth of the iodine containers. Measure-ments are presented as error bars (one standard de-viation statistical uncertainty) and a least-square fit.These are compared to model predictions. . DISCUSSION4.1. Tomosynthesis
The slanted-wire PSF measurement scheme used in this study is associated with some limitations. Firstly, thePSF is not pre-sampled in y , and the wire width is similar to the pixel size. It may be possible to measure a pre-sampled PSF with a wire that is slanted also in y , but that would add uncertainty because of the simultaneousangle in z . As for the wire thickness, thinner wires were found not to provide enough contrast for a reliablemeasurement. Secondly, the PSF is not shift invariant throughout the volume. It differs in z due to differentmagnification factors, and possibly also in y due to different measurement angles. For these reasons, the MTFpresented here should be regarded indicative and not exact.The MTF is not sufficient to fully characterize the system, but should be compared with a noise measurement,ideally in terms of an NPS to form the detective quantum efficiency (DQE) of the system. The NPS has beenmeasured in tomosynthesis in the past, and we are currently preparing a measurement for our system. Futurework also include setting up a model for the full system, to be combined with the presented detector model.
The detector was not perfectly optimized for DES imaging with a fairly large spread in the energy thresholdsand a too low mean value. Moreover, the current anti-coincidence scheme degrades the energy resolution sinceshared photons are put in the high-energy bin, regardless of energy. A better alternative would be to separatecharge shared photons into a third bin, not using them for DES imaging but still saving the information fortransmission images. This study showed that an optimized detector with respect to these deficiencies wouldimprove the subtraction signal substantially, and it is likely that it would perform better also for reducing theanatomical noise. Pile-up was not included in the present detector model, but it is a prioritized upgrade.
5. CONCLUSIONS
We have experimentally characterized a prototype for breast tomosynthesis in terms of the MTF. It is confirmedthat z -resolution is achieved at the cost of y -resolution, whereas x -resolution is unaffected compared to projectionimaging. The full impact of the MTF on detecteability is yet to be determined, but clinical images indicate thatthe trade-off between y and z is justifiable as depth resolution helps increase the conspicuity of breast lesions.The slanted wire approach that was used to measure the MTF gives expected and reasonable results, but themethod is associated with some limitations that need to be taken into account.We further conclude that the new detector work satisfactorily with a high-energy threshold drift that isslow compared to clinical acquisition times, a short dead time, and an acceptable leakage in the AC logic. Theproposed model was successfully verified with experimental results, and predicted that the DES signal differencecan be improved by 38% with a few relatively straightforward improvements. ACKNOWLEDGMENTS
The authors wish to thank Alexander Chuntonov for setting up the silicon-strip detector. Figure 2 is imagecourtesy of the HighReX project.
REFERENCES
1. J. T. 3rd Dobbins and D. J. Godfrey, “Digital x-ray tomosynthesis: current state of the art and clinicalpotential,”
Phys. Med. Biol (19), pp. 65–106, 2003.2. G. Wu, J. G. Mainprize, J. M. Boone, and M. J. Yaffe, “Evaluation of scatter effects on image quality forbreast tomosynthesis,” in Proc. SPIE, Physics of Medical Imaging , M. J. Flynn and J. Hsieh, eds., ,2007.3. Y. H. Hu, B. Zhao, and W. Zhao, “Image artifacts in digital breast tomosynthesis: Investigation of theeffects of system geometry and reconstruction parameters using a linear system approach,”
Med. Phys. (12), pp. 5242–5252, 2008.. P. Johns, D. Drost, M. Yaffe, and A. Fenster, “Dual-energy mammography: initial experimental results,” Med. Phys. , pp. 297–304, 1985.5. J. Lewin, P. Isaacs, V. Vance, and F. Larke, “Dual-energy contrast-enhanced digital subtraction mammog-raphy: Feasibility,” Radiology , pp. 261–268, 2003.6. H. Bornefalk and M. Lundqvist, “Dual-energy imaging using a photon counting detector with electronicspectrum-splitting,” in
Proc. SPIE, Physics of Medical Imaging , M. Flynn and J. Hsieh, eds., , 2006.7. E. Fredenberg, B. Cederstr¨om, M. Lundqvist, C. Ribbing, M. ˚Aslund, F. Diekmann, R. Nishikawa, andM. Danielsson, “Contrast-enhanced dual-energy subtraction imaging using electronic spectrum-splittingand multi-prism x-ray lenses,” in
Proc. SPIE, Physics of Medical Imaging , J. Hsieh and E. Samei, eds.,
Med. Phys. , pp. 933–940, 2006.10. R. N. Cahn, B. Cederstrom, M. Danielsson, A. Hall, M. Lundqvist, and D. Nygren, “Detective quantumefficiency dependence on x-ray energy weighting in mammography,” Med. Phys. (12), pp. 2680–3, 1999.11. M. Lundqvist, Silicon strip detectors for scanned multi-slit x-ray imaging . PhD thesis, Royal Institute ofTechnology (KTH), Stockholm, 2003.12. E. Beuville, B. Cederstr¨om, M. Danielsson, L. Luo, D. Nygren, E. Oltman, and J. Vestlund, “An applicationspecific integrated circuit and data acquisition system for digital x-ray imaging,”
Nucl. Instr. Meth. A ,pp. 337–342, 1998.13. M. ˚Aslund, B. Cederstr¨om, M. Lundqvist, and M. Danielsson, “Physical characterization of a scanningphoton counting digital mammography system based on Si-strip detectors,”
Med. Phys. (6), pp. 1918–1925, 2007.14. K. Lange and J. A. Fessler, “Globally convergent algorithms for maximum a posteriori transmission tomog-raphy,” IEEE Transactions on Image Processing (10), pp. 1430–1438, 2005.15. M. Lundqvist, B. Cederstr¨om, V. Chmill, M. Danielsson, and D. Nygren, “Computer simulations andperformance measurements on a silicon strip detector for edge-on imaging,” IEEE Trans. Nucl. Science (4), pp. 1487–1492, 2000.16. A. Teifke, F. Schweden, H. Cagil, H. Kauczor, W. Mohr, and M. Thelen, “Spiral-Computertomographie derMamma,” Rofo (6), pp. 495–500, 1994.17. J. Boone, “Glandular breast dose for monoenergetic and high-energy x-ray beams: Monte carlo assessment,”
Radiology , pp. 23–37, 1999.18. M. J. Flynn, R. McGee, and J. Blechinger, “Spatial resolution of x-ray tomosynthesis in relation to computedtomography for coronal/sagittal images of the knee,” in
Proc. SPIE, Physics of Medical Imaging , M. Flynnand J. Hsieh, eds., , 2007.19. W. R. Leo,
Techniques for nuclear and particle physics experiments , Springer-Verlag, 1987.20. M. Berger, J. Hubbell, S. Seltzer, J.S., Coursey, and D. Zucker, “XCOM: Photon Cross Section Database.”online: http://physics.nist.gov/xcom. National Institute of Standards and Technology, Gaithersburg, MD,2005.21. K. Israni, G. Avinash, and B. Li, “Point Spread Function based classification of regions for Linear DigitalTomosynthesis,” in
Proc. SPIE, Physics of Medical Imaging , M. Flynn and J. Hsieh, eds.,6510