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  • 1. Boscain, Ugo
    et al.
    Grönberg, Fredrik
    KTH, Skolan för teknikvetenskap (SCI), Fysik.
    Long, Ruixing
    Rabitz, Herschel
    Minimal time trajectories for two-level quantum systems with two bounded controls2014Ingår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 55, nr 6, s. 062106-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we consider the minimum time population transfer problem for a two level quantum system driven by two external fields with bounded amplitude. The controls are modeled as real functions and we do not use the Rotating Wave Approximation. After projection on the Bloch sphere, we treat the time-optimal control problem with techniques of optimal synthesis on 2D manifolds. Based on the Pontryagin Maximum Principle, we characterize a restricted set of candidate optimal trajectories. Properties on this set, crucial for complete optimal synthesis, are illustrated by numerical simulations. Furthermore, when the two controls have the same bound and this bound is small with respect to the difference of the two energy levels, we get a complete optimal synthesis up to a small neighborhood of the antipodal point of the initial condition.

  • 2.
    Boscain, Ugo
    et al.
    CMAP Ecole Polytech, CNRS, Palaiseau, France.;INRIA Saclay, Team GECO, Saclay, France..
    Grönberg, Fredrik
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Medicinsk bildfysik. Linköping Univ, Dept Elect Engn ISY, Linkoping, Sweden..
    Long, Ruixing
    Gen Motors Canada, Oshawa, ON, Canada..
    Rabitz, Herschel
    Princeton Univ, Dept Chem, Princeton, NJ 08544 USA..
    Minimal time trajectories for two-level quantum systems with two bounded controls (vol 55, 062106, 2014)2014Ingår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 55, nr 8, artikel-id 089901Artikel i tidskrift (Refereegranskat)
  • 3.
    da Silva, Joakim
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Medicinsk bildfysik.
    Grönberg, Fredrik
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Medicinsk bildfysik. Prismatic Sensors AB, Stockholm, Sweden.
    Cederström, Björn
    Persson, Mats
    Sjölin, Martin
    Alagic, Zlatan
    Bujila, Robert
    KTH, Skolan för teknikvetenskap (SCI), Fysik. Karolinska University Hospital, Medical Radiation Physics and Nuclear Medicine, Stockholm, Sweden.
    Danielsson, Mats
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Medicinsk bildfysik. Prismatic Sensors AB, Stockholm, Sweden.
    Resolution characterization of a silicon-based, photon-counting computed tomography prototype capable of patient scanning2019Ingår i: Journal of Medical Imaging, ISSN 2329-4302, E-ISSN 2329-4310, Vol. 6, nr 4, artikel-id 043502Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Photon-counting detectors are expected to bring a range of improvements to patient imaging with x-ray computed tomography (CT). One is higher spatial resolution. We demonstrate the resolution obtained using a commercial CT scanner where the original energy-integrating detector has been replaced by a single-slice, silicon-based, photon-counting detector. This prototype constitutes the first full-field-of-view silicon-based CT scanner capable of patient scanning. First, the pixel response function and focal spot profile are measured and, combining the two, the system modulation transfer function is calculated. Second, the prototype is used to scan a resolution phantom and a skull phantom. The resolution images are compared to images from a state-of-the-art CT scanner. The comparison shows that for the prototype 19 lp∕cm are detectable with the same clarity as 14 lp∕cm on the reference scanner at equal dose and reconstruction grid, with more line pairs visible with increasing dose and decreasing image pixel size. The high spatial resolution remains evident in the anatomy of the skull phantom and is comparable to that of other photon-counting CT prototypes present in the literature. We conclude that the deep silicon-based detector used in our study could provide improved spatial resolution in patient imaging without increasing the x-ray dose.

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  • 4.
    Grönberg, Fredrik
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Medicinsk bildfysik.
    Danielsson, Mats
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Medicinsk bildfysik.
    Sjölin, Martin
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Medicinsk bildfysik.
    Count statistics of nonparalyzable photon-counting detectors with nonzero pulse length2018Ingår i: Medical physics (Lancaster), ISSN 0094-2405, Vol. 45, nr 8, s. 3800-3811Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    PurposePhoton-counting detectors are expected to be the next big step in the development of medical computed tomography (CT). Accurate modeling of the behavior of photon-counting detectors in both low and high count rate regimes is important for accurate image reconstruction and detector performance evaluations. The commonly used ideal nonparalyzable (delta pulse) model is built on crude assumptions that make it unsuitable for predicting the behavior of photon-counting detectors at high count rates. The aim of this work is to present an analytical count statistics model that better describes the behavior of photon-counting detectors with nonzero pulse length. MethodsAn analytical statistical count distribution model for nonparalyzable detectors with nonzero pulse length is derived using tools from statistical analysis. To validate the model, a nonparalyzable photon-counting detector is simulated using Monte Carlo methods and compared against. Image performance metrics are computed using the Fisher information metric and a comparison between the proposed model, approximations of the proposed model, and those made by the ideal nonparalyzable model is presented and analyzed. ResultsIt is shown that the presented model agrees well with the results from the Monte Carlo simulation and is stable for varying x-ray beam qualities. It is also shown that a simple Gaussian approximation of the distribution can be used to accurately model the behavior and performance of nonparalyzable detectors with nonzero pulse length. Furthermore, the comparison of performance metrics show that the proposed model predicts a very different behavior than the ideal nonparalyzable detector model, suggesting that the proposed model can fill an important gap in the understanding of pileup effects. ConclusionsAn analytical model for the count statistics of a nonparalyzable photon-counting detector with nonzero pulse length is presented. The model agrees well with results obtained from Monte Carlo simulations and can be used to improve, speed up and simplify modeling of photon-counting detectors.

  • 5.
    Grönberg, Fredrik
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Medicinsk bildfysik.
    Persson, Mats
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Medicinsk bildfysik.
    Bornefalk, Hans
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Medicinsk bildfysik.
    Image reconstruction based on energy-resolved image data from a photon-counting multi-bin detector2015Patent (Övrig (populärvetenskap, debatt, mm))
    Abstract [en]

    There is provided a method of image reconstruction based on energy-resolved image data from a photon-counting multi-bin detector or an intermediate storage. The method comprises processing (S1) the energy-resolved image data by performing at least two separate basis decompositions using different number of basis functions for modeling linear attenuation, wherein a first basis decomposition is performed using a first smaller set of basis functions to obtain at least one first basis image representation, and wherein a second basis decomposition is performed using a second larger set of basis functions to obtain at least one second basis image representation. The method also comprises reconstructing a first image based on said at least one first basis image representation obtained from the first basis decomposition, and combining the first image with information representative of said at least one second basis image representation.

  • 6.
    Grönberg, Fredrik
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Medicinsk bildfysik.
    Persson, Mats
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Medicinsk bildfysik.
    Bornefalk, Hans
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Medicinsk bildfysik.
    Third material separation in spectral CT with basis decomposition2015Konferensbidrag (Övrigt vetenskapligt)
  • 7.
    Grönberg, Fredrik
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Medicinsk bildfysik.
    Sjölin, Martin
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Medicinsk bildfysik.
    Danielsson, Mats
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Medicinsk bildfysik.
    Count statistics and pileup correction for nonparalyzable photon counting detectors with finite pulse length2018Ingår i: Medical Imaging 2018: Physics Of Medical Imaging / [ed] Lo, JY Schmidt, TG Chen, GH, SPIE - International Society for Optical Engineering, 2018, artikel-id UNSP 105730ZKonferensbidrag (Refereegranskat)
    Abstract [en]

    Photon counting detectors are expected to be the next big step in the development of medical computed tomography. Accurate modeling of the behavior of photon counting detectors in the high count rate regime is therefore important for detector performance evaluations and the development of accurate image reconstruction methods. The commonly used ideal nonparalyzable detector model is based on the assumption that photon interactions are converted to pulses with zero extent in time, which is too simplistic to accurately predict the behavior of photon counting detectors in both low and high count rate regimes. In this work we develop a statistical count model for a nonparalyzable detector with finite pulse length and use it to derive the asymptotic mean and variance of the output count distribution using tools from renewal theory. We use the statistical moments of the distribution to construct an estimator of the true number of counts for pileup correction. We con firm the accuracy of the model and evaluate the pileup correction using Monte Carlo simulations. The results show that image quality is preserved for surprisingly high count rates.

  • 8.
    Persson, Mats
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Medicinsk bildfysik.
    Grönberg, Fredrik
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Medicinsk bildfysik.
    Bias-variance tradeoff in anticorrelated noise reduction for spectral CT2017Ingår i: Medical physics (Lancaster), ISSN 0094-2405, Vol. 44, nr 9, s. E242-E254Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Purpose: In spectral CT, basis material decomposition is commonly used to generate a set of basis images showing the material composition at each point in the field of view. The noise in these images typically contains anticorrelations between the different basis images, which leads to increased noise in each basis image. These anticorrelations can be removed by changing the basis functions used in the material decomposition, but the resulting basis images can then no longer be used for quantitative measurements. Recent studies have demonstrated that reconstruction methods which take the anticorrelations into account give reduced noise in the reconstructed image. The purpose of this work is to analyze an analytically solvable denoising model problem and investigate its effect on the noise level and bias in the image as a function of spatial frequency. Method: A denoising problem with a quadratic regularization term is studied as a mathematically tractable model for such a reconstruction method. An analytic formula for the resulting image in the spatial frequency domain is presented, and this formula is applied to a simple mathematical phantom consisting of an iodinated contrast agent insert embedded in soft tissue. We study the effect of the denoising on the image in terms of its transfer function and the visual appearance, the noise power spectrum and the Fourier component correlation coefficient of the resulting image, and compare the result to a denoising problem which does not model the anticorrelations in the image. Results: Including the anticorrelations in the noise model of the denoising method gives 3-40% lower noise standard deviation in the soft-tissue image while leaving the iodine standard deviation nearly unchanged (0-1% difference). It also gives a sharper edge-spread function. The studied denoising method preserves the noise level and the anticorrelated structure at low spatial frequencies but suppresses the noise and removes the anticorrelations at higher spatial frequencies. Cross-talk between images gives rise to artifacts at high spatial frequencies. Conclusions: Modeling anticorrelations in a denoising problem can decrease the noise level in the basis images by removing anticorrelations at high spatial frequencies while leaving low spatial frequencies unchanged. In this way, basis image cross-talk does not lead to low spatial frequency bias but it may cause artifacts at edges in the image. This theoretical insight will be useful for researchers analyzing and designing reconstruction algorithms for spectral CT.

  • 9.
    Persson, Mats
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Medicinsk bildfysik.
    Grönberg, Fredrik
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Medicinsk bildfysik.
    Spatial-frequency-domain study of anticorrelated noise reduction in spectral CT2016Ingår i: CT-Meeting 2016, Proceedings, 2016, s. 283-286Konferensbidrag (Refereegranskat)
  • 10.
    Zheng, Yifan
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Fysik.
    Yveborg, Moa
    Prismat Sensors AB, Roslagstullsbacken 21, S-10691 Stockholm, Sweden..
    Grönberg, Fredrik
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Medicinsk bildfysik.
    Xu, Cheng
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Medicinsk bildfysik.
    Su, Qianqian
    Tsinghua Univ, Minist Educ, Key Lab Particle & Radiat Imaging, Beijing 100084, Peoples R China.;Tsinghua Univ, Dept Engn Phys, Beijing 100084, Peoples R China..
    Danielsson, Mats
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Medicinsk bildfysik.
    Persson, Mats
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Medicinsk bildfysik.
    Robustness of optimal energy thresholds in photon-counting spectral CT2020Ingår i: Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, ISSN 0168-9002, E-ISSN 1872-9576, Vol. 953, artikel-id 163132Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    An important question when developing photon-counting detectors for computed tomography is how to select energy thresholds. In this work thresholds are optimized by maximizing signal-difference-to-noise ratio squared (SDNR2) in an optimally weighted image and signal-to-noise ratio squared (SNR2) in a gadolinium basis image in a silicon-strip detector and a cadmium zinc telluride (CZT) detector, factoring in pileup and imperfect energy response based on real-world detector systems. To investigate to what extent one single set of thresholds could be applied in various imaging tasks, the robustness of optimal thresholds with 2 to 8 bins is examined with the variation of phantom thicknesses, target materials and detector configurations. In contrast to previous studies, the optimal threshold locations do not always increase with increasing attenuation if pileup is included. With respect to the tradeoff between higher SDNR2 or SNR2 and less data, setting optimal thresholds for a 30 cm phantom yields robust SDNR2 and setting optimal thresholds for a 50 cm phantom yields robust SNR2 with 6 to 8 bins in the silicon-strip detector. Furthermore, setting optimal thresholds for a 30 cm phantom yields robust SDNR2 or SNR2 with 6 to 8 bins and a pixel size less than or equal to 0.5 x 0.5 mm(2) in the CZT detector.

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