| 1. |
- Avventi, Enrico, et al.
(författare)
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ARMA Identification of Graphical Models
- 2013
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Ingår i: IEEE Transactions on Automatic Control. - 0018-9286 .- 1558-2523. ; 58:5, s. 1167-1178
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Tidskriftsartikel (refereegranskat)abstract
- Consider a Gaussian stationary stochastic vector process with the property that designated pairs of components are conditionally independent given the rest of the components. Such processes can be represented on a graph where the components are nodes and the lack of a connecting link between two nodes signifies conditional independence. This leads to a sparsity pattern in the inverse of the matrix-valued spectral density. Such graphical models find applications in speech, bioinformatics, image processing, econometrics and many other fields, where the problem to fit an autoregressive (AR) model to such a process has been considered. In this paper we take this problem one step further, namely to fit an autoregressive moving-average (ARMA) model to the same data. We develop a theoretical framework and an optimization procedure which also spreads further light on previous approaches and results. This procedure is then applied to the identification problem of estimating the ARMA parameters as well as the topology of the graph from statistical data.
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| 2. |
- Avventi, Enrico
(författare)
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Divergence-based spectral approximation with degree constraint as a concave optimization problem
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- The Kullback-Leibler pseudo-distance, or divergence, can be used as a criterion for spectral approximation. Unfortunately this criterion is not convex over the most general classes of rational spectra. In this work it will be shown that divergence minimization is equivalent to a costrained entropy minimization problem, whose concave structure can be exploited in order to guarantee global convergence in the most general case.
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| 3. |
- Avventi, Enrico
(författare)
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Divergence-based Spectral Approximation with Degree Constraint as a Concave Optimization Problem
- 2008
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Ingår i: 47TH IEEE CONFERENCE ON DECISION AND CONTROL, 2008 (CDC 2008). - 9781424431243 ; , s. 732-737
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Konferensbidrag (refereegranskat)abstract
- The Kullback-Leibler pseudo-distance, or divergence, can be used as a criterion for spectral approximation. Unfortunately this criterion is not convex over the most general classes of rational spectra. In this work it will be shown that divergence minimization is equivalent to a costrained entropy minimization problem, whose concave structure can be exploited in order to guarantee global convergence in the most general case.
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| 4. |
- Avventi, Enrico
(författare)
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Fast, Globally Converging Algorithms for Spectral Moments Problems
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- In this paper, we consider the matricial version of generalized moment problem with degree constraint. Specifically we focus on computing the solution that minimize the Kullback-Leibler criterion. Several strategies to find such optimum via descent methods are considered and their convergence studied. In particular a parameterization with better numerical properties is derived from a spectral factorization problem. Such parameterization, in addition to guaranteeing descent methods to be globally convergent, it appears to be very reliable in practice.
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| 5. |
- Avventi, Enrico, et al.
(författare)
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Graphical Models of Autoregressive Moving-Average Processes
- 2010
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Ingår i: The 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2010).
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Konferensbidrag (refereegranskat)abstract
- Consider a Gaussian stationary stochastic vector process with the property that designated pairs of components are conditionally independent given the rest of the components. Such processes can be represented on a graph where the components are nodes and the lack of a connecting link between two nodes signifies conditional independence. This leads to a sparsity pattern in the inverse of the matrix-valued spectral density. Such graphical models find applications in speech, bioinformatics, image processing, econometrics and many other fields, where the problem to fit an autoregressive (AR) model to such a process has been considered. In this paper we take this problem one step further, namely to fit an autoregressive moving-average (ARMA) model to the same data. We develop a theoretical framework which also spreads further light on previous approaches and results.
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| 6. |
- Avventi, Enrico, et al.
(författare)
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Projection-based 3D/2D registration for prospective motion correction.
- 2020
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Ingår i: Magnetic Resonance in Medicine. - : Wiley. - 0740-3194 .- 1522-2594. ; 84:3, s. 1534-1542
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Tidskriftsartikel (refereegranskat)abstract
- PURPOSE: To develop a registration method that is capable of estimating the full range of rigid body motion from three orthogonal collapsed images of the head. These images can be obtained using the collapsed FatNav, a previously introduced navigator for prospective motion correction. It combines a short duration with wide compatibility with different main sequences due to its robustness against spin history effects.THEORY AND METHODS: A projection-based 3D/2D registration method is presented and then modified to take into account the peculiarities of the collapsed FatNav. Water/fat separated volumes were used in simulations to assess the accuracy of the proposed method at different resolutions by comparison with high-resolution 3D registration. The sensitivity with respect to masking strategies and starting motion parameters was investigated. Finally, prospective experiments with a healthy volunteer were performed with different types of motion patterns. A PROPELLER main sequence was chosen to compare the prospective correction with PROPELLER's own retrospective correction.RESULTS: In the simulations the proposed method has shown comparable performance to 3D registration. Furthermore, evidence of its robustness with respect to masking strategies and starting motion parameters was presented. The combination with collapsed FatNav has performed well in correcting most of the motion artifacts prospectively with improved image quality compared to only using PROPELLER's retrospective motion correction.CONCLUSIONS: The proposed 3D/2D registration together with collapsed FatNav is characterized by a good balance between navigator duration and estimate accuracy. Further work is needed to validate the method across a wider variety of subject anatomies.
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| 7. |
- Avventi, Enrico, 1980-
(författare)
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Spectral Moment Problems : Generalizations, Implementation and Tuning
- 2011
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Spectral moment interpolation find application in a wide array of use cases: robust control, system identification, model reduction to name the most notable ones. This thesis aims to expand the theory of such methods in three different directions. The first main contribution concerns the practical applicability. From this point of view various solving algorithm and their properties are considered. This study lead to identify a globally convergent method with excellent numerical properties. The second main contribution is the introduction of an extended interpolation problem that allows to model ARMA spectra without any explicit information of zero’s positions. To this end it was necessary for practical reasons to consider an approximated interpolation insted. Finally, the third main contribution is the application to some problems such as graphical model identification and ARMA spectral approximation.
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| 8. |
- Berglund, Johan, et al.
(författare)
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Fat/water separation in k-space with real-valued estimates and its combination with POCS.
- 2020
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Ingår i: Magnetic Resonance in Medicine. - : Wiley. - 0740-3194 .- 1522-2594. ; 83:2, s. 653-661
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Tidskriftsartikel (refereegranskat)abstract
- PURPOSE: To develop reconstruction methods for improved image quality of chemical shift displacement-corrected fat/water imaging combined with partial Fourier acquisition.THEORY: Fat/water separation in k-space enables correction of chemical shift displacement. Modeling fat and water as real-valued rather than complex improves the conditionality of the inverse problem. This advantage becomes essential for k-space separation. In this work, it was described how to perform regularized fat/water imaging with real estimates in k-space, and how fat/water imaging can be combined with partial Fourier reconstruction using Projection Onto Convex Sets (POCS).METHODS: The reconstruction methods were demonstrated on chemical shift encoded gradient echo and fast spin echo data from volunteers, acquired at 1.5 T and 3 T. Both fully sampled and partial Fourier acquisitions were made. Data was retrospectively rejected from the fully sampled dataset to evaluate POCS and homodyne reconstruction.RESULTS: Fat/water separation in k-space eliminated chemical shift displacement, while real-valued estimates considerably reduced the noise amplification compared to complex estimates. POCS reconstruction could recover high spatial frequency information in the fat and water images with lower reconstruction error than homodyne. Partial Fourier in the readout direction enabled more flexible choice of gradient echo imaging parameters, in particular image resolution.CONCLUSION: Chemical shift displacement-corrected fat/water imaging can be performed with regularization and real-valued estimates to improve image quality by reducing ill-conditioning of the inverse problem in k-space. Fat/water imaging can be combined with POCS, which offers improved image quality over homodyne reconstruction.
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| 9. |
- Berglund, Johan, et al.
(författare)
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Motion-insensitive susceptibility weighted imaging.
- 2021
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Ingår i: Magnetic Resonance in Medicine. - : Wiley. - 0740-3194 .- 1522-2594. ; 86:4, s. 1970-1982
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Tidskriftsartikel (refereegranskat)abstract
- PURPOSE: To enable SWI that is robust to severe head movement.METHODS: Prospective motion correction using a markerless optical tracker was applied to all pulse sequences. Three-dimensional gradient-echo and 3D EPI were used as reference sequences, but were expected to be sensitive to motion-induced B0 changes, as the long TE required for SWI allows phase discrepancies to accumulate between shots. Therefore, 2D interleaved snapshot EPI was investigated for motion-robust SWI and compared with conventional 2D EPI. Repeated signal averages were retrospectively corrected for motion. The sequences were evaluated at 3 T through controlled motion experiments involving two cooperative volunteers and SWI of a tumor patient.RESULTS: The performed continuous head motion was in the range of 5-8° rotations. The image quality of the 3D sequences and conventional 2D EPI was poor unless the rotational motion axis was parallel to B0 . Interleaved snapshot EPI had minimal intraslice phase discrepancies due to its small temporal footprint. Phase inconsistency between signal averages was well tolerated due to the high-pass filter effect of the SWI processing. Interleaved snapshot EPI with prospective and retrospective motion correction demonstrated similar image quality, regardless of whether motion was present. Lesion depiction was equal to 3D EPI with matching resolution.CONCLUSION: Susceptibility-based imaging can be severely corrupted by head movement despite accurate prospective motion correction. Interleaved snapshot EPI is a superior alternative for patients who are prone to move and offers SWI which is insensitive to motion when combined with prospective and retrospective motion correction.
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| 10. |
- Berglund, Johan, et al.
(författare)
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Prospective motion correction for diffusion weighted EPI of the brain using an optical markerless tracker.
- 2021
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Ingår i: Magnetic Resonance in Medicine. - : Wiley. - 0740-3194 .- 1522-2594. ; 85:3, s. 1427-1440
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Tidskriftsartikel (refereegranskat)abstract
- PURPOSE: To enable motion-robust diffusion weighted imaging of the brain using well-established imaging techniques.METHODS: An optical markerless tracking system was used to estimate and correct for rigid body motion of the head in real time during scanning. The imaging coordinate system was updated before each excitation pulse in a single-shot EPI sequence accelerated by GRAPPA with motion-robust calibration. Full Fourier imaging was used to reduce effects of motion during diffusion encoding. Subjects were imaged while performing prescribed motion patterns, each repeated with prospective motion correction on and off.RESULTS: Prospective motion correction with dynamic ghost correction enabled high quality DWI in the presence of fast and continuous motion within a 10° range. Images acquired without motion were not degraded by the prospective correction. Calculated diffusion tensors tolerated the motion well, but ADC values were slightly increased.CONCLUSIONS: Prospective correction by markerless optical tracking minimizes patient interaction and appears to be well suited for EPI-based DWI of patient groups unable to remain still including those who are not compliant with markers.
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| 11. |
- Enqvist, Per, et al.
(författare)
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Approximative covariance interpolation with a quadratic penalty
- 2007
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Ingår i: Proceedings Of The 46th IEEE Conference On Decision And Control, Vols 1-14. - 9781424414970 ; , s. 4489-4494
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Konferensbidrag (refereegranskat)abstract
- Given output data of a stationary stochastic process estimates of the covariances parameters can be obtained. These estimates can be used to determine ARMA models to approximatly fit the data by matching the covariances exactly. However, the estimates of the covariances may contain large errors, especially if they are determined from short data sequences, and thus it makes sense to match the covariances only in an approximative way. Here we consider a convex method for solving an approximative covariance interpolation problem while maximizing the entropy and penalize the quadratic deviation from the nominal covariances.
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| 12. |
- Enqvist, Per, et al.
(författare)
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Approximative Linear and Logarithmic Interpolation of Spectra
- 2009
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Given output data of a stationary stochastic process estimates of covariance and cepstrum parameters can be obtained. These estimates can be used to determine ARMA models to approximately fit the data by matching the parameters exactly. However, the estimates of the parameters may contain large errors, especially if they are determined from short data sequences, and thus it makes sense to match the parameters in an approximate way. Here we consider a convex method for solving an approximate linear and logarithmic spectrum interpolation problem while maximizing the entropy and penalize the quadratic deviation from the nominal parameters.
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| 13. |
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| 14. |
- Norbeck, Ola, et al.
(författare)
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Optimizing 3D EPI for rapid T1 -weighted imaging.
- 2020
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Ingår i: Magnetic Resonance in Medicine. - : Wiley. - 0740-3194 .- 1522-2594. ; 84:3, s. 1441-1455
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Tidskriftsartikel (refereegranskat)abstract
- PURPOSE: To investigate the use of 3D EPI for rapid T1 -weighted brain imaging, focusing on the RF pulse's influence on the contrast between gray and white matter.METHODS: An interleaved 3D EPI sequence use partial Fourier and CAIPIRINHA sampling was used to acquire T1 -weighted brain volumes with isotropic resolution, low echo times, and low geometric distortions. Five different RF pulses were evaluated in terms of fat suppression performance and gray-white matter contrast. Two binomial RF pulses were compared to a single rectangular (WE-rect) RF pulse exciting only water, and two new RF pulses developed in this work, where one was an extension of the WE-rect, and the other was an SLR pulse. The technique was demonstrated in three clinical cases, where brain tumor patients were imaged before and after gadolinium administration.RESULTS: A fat-suppressed 3D EPI sequence with a phase encoding bandwidth of around 100 Hz was found to exhibit a good trade-off between geometrical distortions and scan duration. Whole-brain T1 -weighted 3D EPI images with 1.2 mm isotropic voxel size could be acquired in 24 seconds. The WE-rect, its extension, and the SLR RF pulses resulted in reduced magnetization transfer effects and provided a 20% mean increase in gray-white matter contrast.CONCLUSION: Using a high phase encoding bandwidth and RF pulses that reduce magnetization transfer effects, a fat-suppressed multi-shot 3D EPI sequence can be used to rapidly acquire isotropic T1 -weighted volumes.
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| 15. |
- Norbeck, Ola, et al.
(författare)
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T1 -FLAIR imaging during continuous head motion : Combining PROPELLER with an intelligent marker.
- 2021
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Ingår i: Magnetic Resonance in Medicine. - : Wiley. - 0740-3194 .- 1522-2594. ; 85:2, s. 868-882
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Tidskriftsartikel (refereegranskat)abstract
- PURPOSE: The purpose of this work is to describe a T1 -weighted fluid-attenuated inversion recovery (FLAIR) sequence that is able to produce sharp magnetic resonance images even if the subject is moving their head throughout the acquisition.METHODS: The robustness to motion artifacts and retrospective motion correction capabilities of the PROPELLER (periodically rotated overlapping parallel lines with enhanced reconstruction) trajectory were combined with prospective motion correction. The prospective correction was done using an intelligent marker attached to the subject. This marker wirelessly synchronizes to the pulse sequence to measure the directionality and magnitude of the magnetic fields present in the MRI machine during a short navigator, thus enabling it to determine its position and orientation in the scanner coordinate frame. Three approaches to incorporating the marker-navigator into the PROPELLER sequence were evaluated. The specific absorption rate, and subsequent scan time, of the T1 -weighted FLAIR PROPELLER sequence, was reduced using a variable refocusing flip-angle scheme. Evaluations of motion correction performance were done with 4 volunteers and 3 types of head motion.RESULTS: During minimal out-of-plane movement, retrospective PROPELLER correction performed similarly to the prospective correction. However, the prospective clearly outperformed the retrospective correction when there was out-of-plane motion. Finally, the combination of retrospective and prospective correction produced the sharpest images even during large continuous motion.CONCLUSION: Prospective motion correction of a PROPELLER sequence makes it possible to handle continuous, large, and high-speed head motions with only minor reductions in image quality.
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| 16. |
- Rydén, Henric, et al.
(författare)
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Chemical shift encoding using asymmetric readout waveforms.
- 2021
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Ingår i: Magnetic Resonance in Medicine. - : Wiley. - 0740-3194 .- 1522-2594. ; 85:3, s. 1468-1480
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Tidskriftsartikel (refereegranskat)abstract
- PURPOSE: To describe a new method for encoding chemical shift using asymmetric readout waveforms that enables more SNR-efficient fat/water imaging.METHODS: Chemical shift was encoded using asymmetric readout waveforms, rather than conventional shifted trapezoid readouts. Two asymmetric waveforms are described: a triangle and a spline. The concept was applied to a fat/water separated RARE sequence to increase sampling efficiency. The benefits were investigated through comparisons to shifted trapezoid readouts. Using asymmetric readout waveforms, the scan time was either shortened or maintained to increase SNR. A matched in-phase waveform is also described that aims to improve the SNR transfer function of the fat and water estimates. The sequence was demonstrated for cervical spine, musculoskeletal (MSK), and optic nerve applications at 3T and compared with conventional shifted readouts.RESULTS: blurring. Maintaining the scan times and using asymmetric readout waveforms achieved an SNR improvement in agreement with the prolonged sampling duration.CONCLUSIONS: Asymmetric readout waveforms offer an additional degree of freedom in pulse sequence designs where chemical shift encoding is desired. This can be used to significantly shorten scan times or to increase SNR with maintained scan time.
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| 17. |
- Rydén, Henric, et al.
(författare)
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RARE two-point Dixon with dual bandwidths.
- 2020
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Ingår i: Magnetic Resonance in Medicine. - : Wiley. - 0740-3194 .- 1522-2594. ; 84:5, s. 2456-2468
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Tidskriftsartikel (refereegranskat)abstract
- PURPOSE: To investigate the impact of dual readout bandwidths (dBW) in a dual echo fat/water acquisition and describe a dBW-rapid acquisition relaxation enhanced, or turbo spin echo sequence where the concept is used to improve SNR by removing dead times between refocusing pulses and avoiding redundant Chemical-shift encoded.METHODS: Cramér-Rao bounds and Monte Carlo simulations were used to investigate a two-point fat/water model where the difference in bandwidths is incorporated. In vivo images were acquired at 1.5 and 3 T with the dBW-rapid acquisition relaxation enhanced, or turbo spin echo sequence. Typical bandwidth ratios were 1:2. SNR was compared with a single bandwidth sequence under identical scan parameters at 3T.RESULTS: Monte Carlo simulations and Cramér-Rao analysis demonstrate that number of signal averages can be improved with dual bandwidths compared to conventional single bandwidth acquisitions. The dBW-rapid acquisition relaxation enhanced, or turbo spin echo sequence can acquire images with high readout resolutions with well-conditioned sampling. An SNR improvement of 52% was measured, in line with the theoretical gain of 54%.CONCLUSIONS: The proposed dBW-rapid acquisition relaxation enhanced, or turbo spin echo sequence is a highly SNR-efficient two-point rapid acquisition relaxation enhanced, or turbo spin echo sequence without dead times, and can acquire images at higher resolutions than current vendor-supplied alternatives.
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| 18. |
- Rydén, Henric, et al.
(författare)
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T1 weighted fat/water separated PROPELLER acquired with dual bandwidths.
- 2018
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Ingår i: Magnetic Resonance in Medicine. - : Wiley. - 0740-3194 .- 1522-2594. ; 80:6, s. 2501-2513
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Tidskriftsartikel (refereegranskat)abstract
- PURPOSE: To describe a fat/water separated dual receiver bandwidth (rBW) spin echo PROPELLER sequence that eliminates the dead time associated with single rBW sequences. A nonuniform noise whitening by regularization of the fat/water inverse problem is proposed, to enable dual rBW reconstructions.METHODS: Bipolar, flyback, and dual spin echo sequences were developed. All sequences acquire two echoes with different rBW without dead time. Chemical shift displacement was corrected by performing the fat/water separation in k-space, prior to gridding. The proposed sequences were compared to fat saturation, and single rBW sequences, in terms of SNR and CNR efficiency, using clinically relevant acquisition parameters. The impact of motion was investigated.RESULTS: Chemical shift correction greatly improved the image quality, especially at high resolution acquired with low rBW, and also improved motion estimates. SNR efficiency of the dual spin echo sequence was up to 20% higher than the single rBW acquisition, while CNR efficiency was 50% higher for the bipolar acquisition. Noise whitening was deemed necessary for all dual rBW acquisitions, rendering high image quality with strong and homogenous fat suppression.CONCLUSION: Dual rBW sequences eliminate the dead time present in single rBW sequences, which improves SNR efficiency. In combination with the proposed regularization, this enables highly efficient T1-weighted PROPELLER images without chemical shift displacement.
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| 19. |
- Sprenger, Tim, et al.
(författare)
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NeuroMix-A single-scan brain exam
- 2022
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Ingår i: Magnetic Resonance in Medicine. - : Wiley-Blackwell. - 0740-3194 .- 1522-2594. ; 87:5, s. 2178-2193
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Tidskriftsartikel (refereegranskat)abstract
- PURPOSE: Implement a fast, motion-robust pulse sequence that acquires T1 -weighted, T2 -weighted, T2 * -weighted, T2 fluid-attenuated inversion recovery, and DWI data in one run with only one prescription and one prescan.METHODS: A software framework was developed that configures and runs several sequences in one main sequence. Based on that framework, the NeuroMix sequence was implemented, containing motion robust single-shot sequences using EPI and fast spin echo (FSE) readouts (without EPI distortions). Optional multi-shot sequences that provide better contrast, higher resolution, or isotropic resolution could also be run within the NeuroMix sequence. An optimized acquisition order was implemented that minimizes times where no data is acquired.RESULTS: NeuroMix is customizable and takes between 1:20 and 4 min for a full brain scan. A comparison with the predecessor EPIMix revealed significant improvements for T2 -weighted and T2 fluid-attenuated inversion recovery, while taking only 8 s longer for a similar configuration. The optional contrasts were less motion robust but offered a significant increase in quality, detail, and contrast. Initial clinical scans on 1 pediatric and 1 adult patient showed encouraging image quality.CONCLUSION: The single-shot FSE readouts for T2 -weighted and T2 fluid-attenuated inversion recovery and the optional multishot FSE and 3D-EPI contrasts significantly increased diagnostic value compared with EPIMix, allowing NeuroMix to be considered as a standalone brain MRI application.
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| 20. |
- van Niekerk, Adam, et al.
(författare)
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Control of a wireless sensor using the pulse sequence for prospective motion correction in brain MRI.
- 2022
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Ingår i: Magnetic Resonance in Medicine. - : Wiley. - 0740-3194 .- 1522-2594. ; 87:2, s. 1046-1061
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Tidskriftsartikel (refereegranskat)abstract
- PURPOSE: To synchronize and pass information between a wireless motion-tracking device and a pulse sequence and show how this can be used to implement customizable navigator interleaving schemes that are part of the pulse sequence design.METHODS: The device tracks motion by sampling the voltages induced in 3 orthogonal pickup coils by the changing gradient fields. These coils were modified to also detect RF-transmit events using a 3D RF-detection circuit. The device could then detect and decode a set RF signatures while ignoring excitations in the parent pulse sequence. A set of unique RF signatures were then paired with a collection of navigators and used to trigger readouts on the wireless device synchronous to the pulse sequence execution. Navigator interleaving schemes were then demonstrated in 3D RF-spoiled gradient echo, T1 -FLAIR (fluid-attenuated inversion recovery) PROPELLER (periodically rotated overlapping parallel lines with enhanced reconstruction), and T2 -FLAIR PROPELLER pulse sequences.RESULTS: Excitations in the parent pulse sequences were successfully rejected and the RF signatures successfully decoded. For the 3D gradient echo sequence, distortions were removed by interleaving flipped polarity navigators and taking the difference between consecutive readouts. The impact on scan duration was reduced by 54% by breaking up the navigators into smaller parts. Successful motion correction was performed using the PROPELLER pulse sequences in 3 Tesla and 1.5 Tesla MRI scanners without modifications to the device hardware or software.CONCLUSION: The proposed RF signature-based triggering scheme enables complex interactions between the pulse sequence and a wireless device. Thus, enabling prospective motion correction that is repeatable, versatile, and minimally invasive with respect to hardware setup.
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