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  • 1.
    Björk, Marcus
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Contributions to Signal Processing for MRI2015Doctoral thesis, monograph (Other academic)
    Abstract [en]

    Magnetic Resonance Imaging (MRI) is an important diagnostic tool for imaging soft tissue without the use of ionizing radiation. Moreover, through advanced signal processing, MRI can provide more than just anatomical information, such as estimates of tissue-specific physical properties.

    Signal processing lies at the very core of the MRI process, which involves input design, information encoding, image reconstruction, and advanced filtering. Based on signal modeling and estimation, it is possible to further improve the images, reduce artifacts, mitigate noise, and obtain quantitative tissue information.

    In quantitative MRI, different physical quantities are estimated from a set of collected images. The optimization problems solved are typically nonlinear, and require intelligent and application-specific algorithms to avoid suboptimal local minima. This thesis presents several methods for efficiently solving different parameter estimation problems in MRI, such as multi-component T2 relaxometry, temporal phase correction of complex-valued data, and minimizing banding artifacts due to field inhomogeneity. The performance of the proposed algorithms is evaluated using both simulation and in-vivo data. The results show improvements over previous approaches, while maintaining a relatively low computational complexity. Using new and improved estimation methods enables better tissue characterization and diagnosis.

    Furthermore, a sequence design problem is treated, where the radio-frequency excitation is optimized to minimize image artifacts when using amplifiers of limited quality. In turn, obtaining higher fidelity images enables improved diagnosis, and can increase the estimation accuracy in quantitative MRI.

  • 2.
    Björk, Marcus
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Berglund, Johan
    Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Medicine, Department of Radiology, Oncology and Radiation Science, Radiology.
    Kullberg, Joel
    Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Medicine, Department of Radiology, Oncology and Radiation Science, Radiology.
    Stoica, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Signal Modeling and the Cramér-Rao Bound for Absolute Magnetic Resonance Thermometry in Fat Tissue2011In: Proc. 45th Asilomar Conference on Signals, Systems, and Computers, 2011, p. 80-84Conference paper (Refereed)
    Abstract [en]

    Magnetic Resonance Imaging of tissues with both fat and water resonances allows for absolute temperature mapping through parametric modeling. The fat resonance is used as a reference to determine the absolute water resonance frequency which is linearly related to the temperature. The goal of thispaper is to assess whether or not resonance frequency based absolute temperature mapping is feasible in fat tissue. This is done by examining identifiability conditions and analyzing the obtainable performance in terms of the Cramér-Rao Bound of the temperature estimates. We develop the model by including multiple fat peaks, since even small fat resonances can be significant compared to the small water component in fat tissue. It is showed that a high signal to noise ratio is needed for practical use on a 1.5 T scanner, and that higher field strengths can improve the bound significantly. It is also shown that the choice of sampling interval is important to avoid aliasing. In sum, this type of magnetic resonance thermometry is feasible for fat tissuein applications where high field strength is used or when high signal to noise ratio can be obtained.

  • 3.
    Björk, Marcus
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Gudmundson, Erik
    Centre for Mathematical Sciences, Lund University.
    Barral, Joëlle
    Department of Bioengineering, Stanford University.
    Stoica, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Signal Processing Algorithms for Removing Banding Artifacts in MRI2011In: Proceedings of the 19th European Signal Processing Conference (EUSIPCO-2011), 2011, p. 1000-1004Conference paper (Refereed)
    Abstract [en]

    In magnetic resonance imaging (MRI), the balanced steady-state free precession (bSSFP) pulse sequence has shown to be of great interest, due to its relatively high signal-to-noise ratio in a short scan time. However, images acquired with this pulse sequence suffer from banding artifacts due to off-resonance effects. These artifacts typically appear as black bands covering parts of the image and they severely degrade the image quality. In this paper, we present a fast two-step algorithm for estimating the unknowns in the signal model and removing the banding artifacts. The first step consists of rewriting the model in such a way that it becomes linear in the unknowns (this step is named Linearization for Off-Resonance Estimation, or LORE). In the second step, we use a Gauss-Newton iterative optimization with the parameters obtained by LORE as initial guesses. We name the full algorithm LORE-GN. Using both simulated and in vivo data, we show the performance gain associated with using LORE-GN as compared to general methods commonly employed in similar cases.

  • 4.
    Björk, Marcus
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Ingle, R. Reeve
    Electrical Engineering, Stanford University, Stanford, California, United States.
    Barral, Joëlle K.
    HeartVista, Inc., Los Altos, California, USA.
    Gudmundson, Erik
    Centre for Mathematical Sciences, Lund University.
    Nishimura, Dwight G.
    Electrical Engineering, Stanford University, Stanford, California, United States.
    Stoica, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Optimality of Equally-Spaced Phase Increments for Banding Removal in bSSFP2012In: Proceedings of the ISMRM 20th annual meeting, 2012Conference paper (Refereed)
  • 5.
    Björk, Marcus
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Ingle, R. Reeve
    Gudmundson, Erik
    Stoica, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Nishimura, Dwight G.
    Barral, Joëlle K.
    Parameter estimation approach to banding artifact reduction in balanced steady-state free precession2014In: Magnetic Resonance in Medicine, ISSN 0740-3194, E-ISSN 1522-2594, Vol. 72, no 3, p. 880-892Article in journal (Refereed)
    Abstract [en]

    Purpose: The balanced steady-state free precession (bSSFP) pulse sequence has shown to be of great interest due to its high signal-to-noise ratio efficiency. However, bSSFP images often suffer from banding artifacts due to off-resonance effects, which we aim to minimize in this article. Methods: We present a general and fast two-step algorithm for 1) estimating the unknowns in the bSSFP signal model from multiple phase-cycled acquisitions, and 2) reconstructing band-free images. The first step, linearization for off-resonance estimation (LORE), solves the nonlinear problem approximately by a robust linear approach. The second step applies a Gauss-Newton algorithm, initialized by LORE, to minimize the nonlinear least squares criterion. We name the full algorithm LORE-GN. Results: We derive the Cramer-Rao bound, a theoretical lower bound of the variance for any unbiased estimator, and show that LORE-GN is statistically efficient. Furthermore, we show that simultaneous estimation of T-1 and T-2 from phase-cycled bSSFP is difficult, since the Cramer-Rao bound is high at common signal-to-noise ratio. Using simulated, phantom, and in vivo data, we illustrate the band-reduction capabilities of LORE-GN compared to other techniques, such as sum-of-squares. Conclusion: Using LORE-GN we can successfully minimize banding artifacts in bSSFP.

  • 6.
    Björk, Marcus
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Medvedev, Alexander
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Estimation of dynamic models with output quantization applied to drug response modeling2010Conference paper (Other academic)
  • 7.
    Björk, Marcus
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Medvedev, Alexander
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Stoica, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Dynamic models with quantized output for modeling patient response to pharmacotherapy2010In: Proc. International Conference on Control Applications: CCA 2010, Piscataway, NJ: IEEE , 2010, p. 1029-1034Conference paper (Refereed)
    Abstract [en]

    This article presents a way of modeling patient response to a pharmacotherapy by means of dynamic models with quantized output. The proposed modeling technique is exemplified by treatment of Parkinson's disease with Duodopa ®, where the drug is continuously administered via duodenal infusion. Titration of Duodopa ® is currently performed manually by a nurse judging the patient's motor symptoms on a quantized scale and adjusting the drug flow provided by a portable computer-controlled infusion pump. The optimal drug flow value is subject to significant inter-individual variation and the titration process might take up to two weeks for some patients. In order to expedite the titration procedure via automation, as well as to find optimal dosing strategies, a mathematical model of this system is sought. The proposed model is of Wiener type with a linear dynamic block, cascaded with a static nonlinearity in the form of a non-uniform quantizer where the quantizer levels are to be identified. An identification procedure based on the prediction error method and the Gauss-Newton algorithm is suggested. The datasets available from titration sessions are scarce so that finding a parsimonious model is essential. A few different model parameterizations and identification algorithms were initially evaluated. The results showed that models with four parameters giving accurate predictions can be identified for some of the available datasets.

  • 8.
    Björk, Marcus
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Stoica, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Fast denoising techniques for transverse relaxation time estimation in MRI2013In: Proc. 21st European Signal Processing Conference, 2013Conference paper (Refereed)
  • 9.
    Björk, Marcus
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Stoica, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Magnitude-constrained sequence design with application in MRI2014In: Proc. 39th IEEE International Conference on Acoustics, Speech, and Signal Processing, Piscataway, NJ: IEEE , 2014, p. 4943-4947Conference paper (Refereed)
    Abstract [en]

    In this paper we present an algorithm for sequence design with magnitude constraints. We formulate the design problem in a general setting, but also illustrate its relevance to parallel excitation MRI. The formulated non-convex design optimization criterion is minimized locally by means of a cyclic algorithm, consisting of two simple algebraic sub-steps. Since the algorithm truly minimizes the criterion, the obtained sequence designs are guaranteed to improve upon the estimates provided by a previous method, which is based on the heuristic principle of the Iterative Quadratic Maximum Likelihood algorithm. The performance of the proposed algorithm is illustrated in two numerical examples.

  • 10.
    Björk, Marcus
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Stoica, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    New approach to phase correction in multi-echo T2 relaxometry2014In: Journal of magnetic resonance, ISSN 1090-7807, E-ISSN 1096-0856, Vol. 249, p. 100-107Article in journal (Refereed)
    Abstract [en]

    Estimation of the transverse relaxation time, T-2, from multi-echo spin-echo images is usually performed using the magnitude of the noisy data, and a least squares (LS) approach. The noise in these magnitude images is Rice distributed, which can lead to a considerable bias in the LS-based T-2 estimates. One way to avoid this bias problem is to estimate a real-valued and Gaussian distributed dataset from the complex data, rather than using the magnitude. In this paper, we propose two algorithms for phase correction which can be used to generate real-valued data suitable for LS-based parameter estimation approaches. The first is a Weighted Linear Phase Estimation algorithm, abbreviated as WELPE. This method provides an improvement over a previously published algorithm, while simplifying the estimation procedure and extending it to support multi-coil input. The algorithm fits a linearly parameterized function to the multi-echo phase-data in each voxel and, based on this estimated phase, projects the data onto the real axis. The second method is a maximum likelihood estimator of the true decaying signal magnitude, which can be efficiently implemented when the phase variation is linear in time. The performance of the algorithms is demonstrated via Monte Carlo simulations, by comparing the accuracy of the estimates. Furthermore, it is shown that using one of the proposed algorithms enables more accurate T-2 estimates; in particular, phase corrected data significantly reduces the estimation bias in multi-component T-2 relaxometry example, compared to when using magnitude data. WELPE is also applied to a 32-echo in vivo brain dataset, to show its practical feasibility.

  • 11.
    Björk, Marcus
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Zachariah, Dave
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Kullberg, Joel
    Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Medicine, Department of Surgical Sciences, Radiology.
    Stoica, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    A multicomponent T2 relaxometry algorithm for myelin water imaging of the brain2016In: Magnetic Resonance in Medicine, ISSN 0740-3194, E-ISSN 1522-2594, Vol. 75, no 1, p. 390-402Article in journal (Refereed)
  • 12.
    Ingle, R. Reeve
    et al.
    Electrical Engineering, Stanford University, Stanford, California, United States.
    Barral, Joëlle K.
    HeartVista, Inc., Los Altos, California, USA.
    Björk, Marcus
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Gudmundson, Erik
    Centre for Mathematical Sciences, Lund University.
    Stoica, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Nishimura, Dwight G.
    Electrical Engineering, Stanford University, Stanford, California, United States.
    SNR Requirements for T1 and T2 Estimation using bSSFP2012In: Proceedings of the ISMRM 20th annual meeting, 2012Conference paper (Refereed)
  • 13.
    Ramos-Llordén, Gabriel
    et al.
    Department of Physics, Imec-Vision Lab, University of Antwerp, Antwerp, Belgium.
    Vegas-Sánchez-Ferrero, Gonzalo
    Applied Chest Imaging Laboratory, Brigham and Women’s Hospital, Harvard Medical School, Boston, MA, USA .
    Björk, Marcus
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Vanhevel, Floris
    Department of Radiology, University of Antwerp, Antwerp University Hospital, Antwerp, Belgium.
    Parizel, Paul M.
    Department of Radiology, University of Antwerp, Antwerp University Hospital, Antwerp, Belgium.
    San José Estépar, Raúl
    Applied Chest Imaging Laboratory, Brigham and Women’s Hospital, Harvard Medical School, Boston, MA, USA.
    den Dekker, Arnold J.
    Department of Physics, Imec-Vision Lab, University of Antwerp, Antwerp, Belgium.
    Sijbers, Jan
    Department of Physics, Imec-Vision Lab, University of Antwerp, Antwerp, Belgium.
    NOVIFAST: A Fast Algorithm for Accurate and Precise VFA MRIT1Mapping2018In: IEEE Transactions on Medical Imaging, ISSN 0278-0062, E-ISSN 1558-254X, Vol. 37, no 11, p. 2414-2427Article in journal (Refereed)
    Abstract [en]

    In quantitative magnetic resonance T 1 mapping, the variable flip angle (VFA) steady state spoiled gradient recalled echo (SPGR) imaging technique is popular as it provides a series of high resolution T 1 weighted images in a clinically feasible time. Fast, linear methods that estimate T 1 maps from these weighted images have been proposed, such as DESPOT1 and iterative re-weighted linear least squares. More accurate, non-linear least squares (NLLS) estimators are in play, but these are generally much slower and require careful initialization. In this paper, we present NOVIFAST, a novel NLLS-based algorithm specifically tailored to VFA SPGR T 1 mapping. By exploiting the particular structure of the SPGR model, a computationally efficient, yet accurate and precise T 1 map estimator is derived. Simulation and in vivo human brain experiments demonstrate a twenty-fold speed gain of NOVIFAST compared with conventional gradient-based NLLS estimators while maintaining a high precision and accuracy. Moreover, NOVIFAST is eight times faster than the efficient implementations of the variable projection (VARPRO) method. Furthermore, NOVIFAST is shown to be robust against initialization.

1 - 13 of 13
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