| 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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