| 1. |
- Sume, Ain, et al.
(författare)
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Radar Detection of Moving Targets Behind Corners
- 2011
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Ingår i: IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING. - : IEEE; 1999. - 0196-2892. ; 49:6, s. 2259-2267
-
Tidskriftsartikel (refereegranskat)abstract
- Detection of moving objects concealed behind a concrete wall corner has been demonstrated, using Doppler-based techniques with a stepped-frequency radar centered at 10 GHz, in a reduced-scale model of a street scenario. Micro-Doppler signatures have been traced in the return from a human target, both for walking and for breathing. Separate material measurements of the reflection and transmission of the concrete in the wall have showed that wall reflections are the dominating wave propagation mechanism for producing target detections, while wave components transmitted through the walls could be neglected. Weaker detections have been made of target returns via diffraction in the wall corner. A simple and fast algorithm for the detection and generation of detection tracks in down range has been developed, based on moving target indication technique.
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| 2. |
- Bergman Ärlebäck, Jonas, 1972-
(författare)
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Conformal Einstein spaces and Bach tensor generalization in n dimensions
- 2004
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis we investigate necessary and su±cient conditions for an n-dimensional space, n ≥ 4, to be locally conformal to an Einstein space. After reviewing the classical results derived in tensors we consider the four-dimensional spinor result of Kozameh, Newman and Tod. The involvement of the four-dimensional Bach tensor (which is divergence-free and conformally well-behaved) in their result motivates a search for an n-dimensional generalization of the Bach tensor Bab with the same properties. We strengthen a theorem due to Belfagón and Jaén and give a basis (Uab, V ab and Wab) for all n-dimensional symmetric, divergence-free 2-index tensors quadratic in the Riemann curvature tensor. We discover the simple relationship Bab = 1/2Uab + 1/6V ab and show that the Bach tensor is the unique tensor with these properties in four dimensions. Unfortunately we have to conclude, in general that there is no direct analogue in higher dimension with all these properties.Nevertheless, we are able to generalize the our-dimensional results due to Kozameh, Newman and Tod to n dimensions. We show that a generic space is conformal to an Einstein space if and only if there exists a vector field satisfying two conditions. The explicit use of dimensionally dependent identities (some of which are newly derived in this thesis) is also exploited in order to make the two conditions as simple as possible; explicit examples are given in five and six dimensions using these tensor identities. For n dimensions, we define the tensors babc and Bab, and we show that their vanishing is a conformal invariant property which guarantees that the space with non-degenerate Weyl tensor is a conformal Einstein space.
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| 3. |
- Bergman Ärlebäck, Jonas, 1972-, et al.
(författare)
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The Bach tensor and other divergence-free tensors
- 2005
-
Ingår i: International Journal of Geometric Methods in Modern Physics (IJGMMP). - 0219-8878. ; 2:1, s. 13-21
-
Tidskriftsartikel (refereegranskat)abstract
- In four dimensions, we prove that the Bach tensor is the only symmetric divergence-free 2-tensor which is also quadratic in Riemann and has good conformal behavior. In n > 4 dimensions, we prove that there are no symmetric divergence-free 2-tensors which are also quadratic in Riemann and have good conformal behavior, nor are there any symmetric divergence-free 2-tensors which are concomitants of the metric tensor gab together with its first two derivatives, and have good conformal behavior.
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| 4. |
- Boito, Deneb, et al.
(författare)
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Applying positivity constraints to q-space traj ectory imaging : The QTI plus implementation
- 2022
-
Ingår i: SoftwareX. - : Elsevier. - 2352-7110. ; 18
-
Tidskriftsartikel (refereegranskat)abstract
- Diffusion MRI is a powerful technique sensitive to the microstructure of heterogeneous media. By relating the dMRI signal obtained via general gradient waveforms to the moments of an underlying diffusion tensor distribution, q-space trajectory imaging (QTI) provides several quantities indicative of the structural composition of the medium. Substantial improvements in the reliability of the produced estimates has been achieved via incorporating necessary positivity constraints in the estimation by employing Semidefinite Programming. Here we present the Matlab code implementing said constraints, provide a simple example showing the main functionalities of the package, and point to resources within the package that can be used to reproduce results recently published with this software. The block-based structure of our implementation allows the selection of steps to be performed, and facilitates the incorporation of new constraints in future releases.
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| 5. |
- Boito, Deneb, 1993-
(författare)
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Diffusion MRI with generalised gradient waveforms : methods, models, and neuroimaging applications
- 2023
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The incessant, random motion of water molecules within biological tissues reveals unique information about the tissues’ structural and functional characteristics. Diffusion magnetic resonance imaging is sensitive to this random motion, and since the mid-1990s it has been extensively employed for studying the human brain. Most notably, measurements of water diffusion allow for the early detection of ischaemic stroke and for the unveiling of the brain’s wiring via reconstruction of the neuronal connections. Ultimately, the goal is to employ this imaging technique to perform non-invasive, in vivo virtual histology to directly characterise both healthy and diseased tissue. Recent developments in the field have introduced new ways to measure the diffusion process in clinically feasible settings. These new measurements, performed by employing generalised magnetic field gradient waveforms, grant access to specific features of the cellular composition and structural organisation of the tissue. Methods based on them have already proven beneficial for the assessment of different brain diseases, sparking interest in translating such techniques into clinical practice. This thesis focuses on improving the methods currently employed for the analysis of such diffusion MRI data, with the aim of facilitating their clinical adoption. The first two publications introduce constrained frameworks for the estimation of parameters from diffusion MRI data acquired with generalised gradient waveforms. The constraints are dictated by mathematical and physical properties of a multi-compartment model used to represent the brain tissue, and can be efficiently enforced by employing a relatively new optimisation scheme called semidefinite programming. The developed routines are demonstrated to improve robustness to noise and imperfect data collection. Moreover, constraining the fit is shown to relax the requirements on the number of points needed for the estimation, thus allowing for faster data acquisition. In the third paper, the developed frameworks are employed to study the brain’s white matter in patients previously hospitalised for COVID-19 and who still suffer from neurological symptoms months after discharge. The results show widespread alterations to the structural integrity of their brain, with the metrics available through the advanced diffusion measurements providing new insights into the damage to the white matter. The fourth paper revisits the modelling paradigm currently adopted for the analysis of diffusion MRI data acquired with generalised gradient waveforms. Hitherto, the assumption of free diffusion has been employed to represent each domain in a multi-compartmental picture of the brain tissue. In this work, a model for restricted diffusion is considered instead to alleviate the paradoxical assumption of free but compartmentalised diffusion. The model is shown to perfectly capture restricted diffusion as measured with the generalised diffusion gradient waveforms, thus endorsing its use for representing each domain in the multi-compartmental model of the tissue.
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| 6. |
- Boito, Deneb, 1993-, et al.
(författare)
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Diffusivity-limited q-space trajectory imaging
- 2023
-
Ingår i: Magnetic Resonance Letters. - : KeAi Publishing Communications. - 2772-5162. ; 3:2, s. 187-196
-
Tidskriftsartikel (refereegranskat)abstract
- Q-space trajectory imaging (QTI) allows non-invasive estimation of microstructural features of heterogeneous porous media via diffusion magnetic resonance imaging performed with generalised gradient waveforms. A recently proposed constrained estimation framework, called QTI+, improved QTI’s resilience to noise and data sparsity, thus increasing the reliability of the method by enforcing relevant positivity constraints. In this work we consider expanding the set of constraints to be applied during the fitting of the QTI model. We show that the additional conditions, which introduce an upper bound on the diffusivity values, further improve the retrieved parameters on a publicly available human brain dataset as well as on data acquired from healthy volunteers using a scanner-ready protocol.
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| 7. |
- Brun, Anders, 1976-, et al.
(författare)
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Fast manifold learning based on Riemannian normal coordinates
- 2005
-
Ingår i: Image Analysis. - Berlin, Heidelberg : Springer Berlin/Heidelberg. - 9783540263203 - 9783540315667 ; , s. 920-
-
Konferensbidrag (refereegranskat)abstract
- We present a novel method for manifold learning, i.e. identification of the low-dimensional manifold-like structure present in a set of data points in a possibly high-dimensional space. The main idea is derived from the concept of Riemannian normal coordinates. This coordinate system is in a way a generalization of Cartesian coordinates in Euclidean space. We translate this idea to a cloud of data points in order to perform dimension reduction. Our implementation currently uses Dijkstra’s algorithm for shortest paths in graphs and some basic concepts from differential geometry. We expect this approach to open up new possibilities for analysis of e.g. shape in medical imaging and signal processing of manifold-valued signals, where the coordinate system is “learned” from experimental high-dimensional data rather than defined analytically using e.g. models based on Lie-groups.
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| 8. |
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| 9. |
- Brun, Anders, 1976-, et al.
(författare)
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Intrinsic and Extrinsic Means on the Circle -- a Maximum Likelihood Interpretation
- 2007
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Ingår i: ICASSP 2007. IEEE International Conference on Acoustics, Speech and Signal Processing, 2007. - New York, USA : IEEE. - 1424407273 ; , s. III-1053-III-1056
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Konferensbidrag (refereegranskat)abstract
- For data samples in Rn, the mean is a well known estimator. When the data set belongs to an embedded manifold M in Rn, e.g. the unit circle in R2, the definition of a mean can be extended and constrained to M by choosing either the intrinsic Riemannian metric of the manifold or the extrinsic metric of the embedding space. A common view has been that extrinsic means are approximate solutions to the intrinsic mean problem. This paper study both means on the unit circle and reveal how they are related to the ML estimate of independent samples generated from a Brownian distribution. The conclusion is that on the circle, intrinsic and extrinsic means are maximum likelihood estimators in the limits of high SNR and low SNR respectively
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| 10. |
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| 11. |
- Brun, Anders, 1976-
(författare)
-
Manifold learning and representations for image analysis and visualization
- 2006
-
Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- We present a novel method for manifold learning, i.e. identification of the low-dimensional manifold-like structure present in a set of data points in a possibly high-dimensional space. The main idea is derived from the concept of Riemannian normal coordinates. This coordinate system is in a way a generalization of Cartesian coordinates in Euclidean space. We translate this idea to a cloud of data points in order to perform dimension reduction. Our implementation currently uses Dijkstra's algorithm for shortest paths in graphs and some basic concepts from differential geometry. We expect this approach to open up new possibilities for analysis of e.g. shape in medical imaging and signal processing of manifold-valued signals, where the coordinate system is “learned” from experimental high-dimensional data rather than defined analytically using e.g. models based on Lie-groups.We propose a novel post processing method for visualization of fiber traces from DT-MRI data. Using a recently proposed non-linear dimensionality reduction technique, Laplacian eigenmaps (Belkin and Niyogi, 2002), we create a mapping from a set of fiber traces to a low dimensional Euclidean space. Laplacian eigenmaps constructs this mapping so that similar traces are mapped to similar points, given a custom made pairwise similarity measure for fiber traces. We demonstrate that when the low-dimensional space is the RGB color space, this can be used to visualize fiber traces in a way which enhances the perception of fiber bundles and connectivity in the human brain.
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| 12. |
- Brun, Anders, 1976-
(författare)
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Manifolds in Image Science and Visualization
- 2007
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- A Riemannian manifold is a mathematical concept that generalizes curved surfaces to higher dimensions, giving a precise meaning to concepts like angle, length, area, volume and curvature. A glimpse of the consequences of a non-flat geometry is given on the sphere, where the shortest path between two points – a geodesic – is along a great circle. Different from Euclidean space, the angle sum of geodesic triangles on the sphere is always larger than 180 degrees.Signals and data found in applied research are sometimes naturally described by such curved spaces. This dissertation presents basic research and tools for the analysis, processing and visualization of such manifold-valued data, with a particular emphasis on future applications in medical imaging and visualization.Two-dimensional manifolds, i.e. surfaces, enter naturally into the geometric modelling of anatomical entities, such as the human brain cortex and the colon. In advanced algorithms for processing of images obtained from computed tomography (CT) and ultrasound imaging (US), images themselves and derived local structure tensor fields may be interpreted as two- or three-dimensional manifolds. In diffusion tensor magnetic resonance imaging (DT-MRI), the natural description of diffusion in the human body is a second-order tensor field, which can be related to the metric of a manifold. A final example is the analysis of shape variations of anatomical entities, e.g. the lateral ventricles in the brain, within a population by describing the set of all possible shapes as a manifold.Work presented in this dissertation include: Probabilistic interpretation of intrinsic and extrinsic means in manifolds. A Bayesian approach to filtering of vector data, removing noise from sampled manifolds and signals. Principles for the storage of tensor field data and learning a natural metric for empirical data.The main contribution is a novel class of algorithms called LogMaps, for the numerical estimation of logp (x) from empirical data sampled from a low-dimensional manifold or geometric model embedded in Euclidean space. The logp (x) function has been used extensively in the literature for processing data in manifolds, including applications in medical imaging such as shape analysis. However, previous approaches have been limited to manifolds where closed form expressions of logp (x) have been known. The introduction of the LogMap framework allows for a generalization of the previous methods. The application of LogMaps to texture mapping, tensor field visualization, medial locus estimation and exploratory data analysis is also presented.
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| 13. |
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| 14. |
- Brun, Anders, 1976-, et al.
(författare)
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Similar Tensor Arrays : A Framework for Storage of Tensor Array Data
- 2009. - 1
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Ingår i: Tensors in Image Processing and Computer Vision. - London : Springer. - 9781848822986 - 9781848822993 ; , s. 407-428
-
Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- Abstract This chapter describes a framework for storage of tensor array data, useful to describe regularly sampled tensor fields. The main component of the framework, called Similar Tensor Array Core (STAC), is the result of a collaboration between research groups within the SIMILAR network of excellence. It aims to capture the essence of regularly sampled tensor fields using a minimal set of attributes and can therefore be used as a “greatest common divisor” and interface between tensor array processing algorithms. This is potentially useful in applied fields like medical image analysis, in particular in Diffusion Tensor MRI, where misinterpretation of tensor array data is a common source of errors. By promoting a strictly geometric perspective on tensor arrays, with a close resemblance to the terminology used in differential geometry, (STAC) removes ambiguities and guides the user to define all necessary information. In contrast to existing tensor array file formats, it is minimalistic and based on an intrinsic and geometric interpretation of the array itself, without references to other coordinate systems.
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| 15. |
- Brun, Anders, 1976-, et al.
(författare)
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Using Importance Sampling for Bayesian Feature Space Filtering
- 2007
-
Ingår i: Proceedings of the 15th Scandinavian conference on image analysis. - Berlin, Heidelberg : Springer-Verlag. - 9783540730392 ; , s. 818-827
-
Konferensbidrag (refereegranskat)abstract
- We present a one-pass framework for filtering vector-valued images and unordered sets of data points in an N-dimensional feature space. It is based on a local Bayesian framework, previously developed for scalar images, where estimates are computed using expectation values and histograms. In this paper we extended this framework to handle N-dimensional data. To avoid the curse of dimensionality, it uses importance sampling instead of histograms to represent probability density functions. In this novel computational framework we are able to efficiently filter both vector-valued images and data, similar to e.g. the well-known bilateral, median and mean shift filters.
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| 16. |
- Bäckdahl, Thomas, et al.
(författare)
-
Calculation of, and bounds for, the multipole moments of stationary spacetimes
- 2006
-
Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 23:20, s. 5997-6006
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper, the multipole moments of stationary asymptotically flat spacetimes are considered. We show how the tensorial recursion of Geroch and Hansen can be replaced by a scalar recursion on . We also give a bound on the multipole moments. This gives a proof of the 'necessary part' of a long-standing conjecture due to Geroch.
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| 17. |
- Bäckdahl, Thomas, et al.
(författare)
-
Explicit multipole moments of stationary axisymmetric spacetimes
- 2005
-
Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 22:17, s. 3585-3594
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper, we study multipole moments of axisymmetric stationary asymptotically flat spacetimes. We show how the tensorial recursion of Geroch and Hansen can be reduced to a recursion of scalar functions. We also demonstrate how a careful choice of conformal factor collects all moments into one complex-valued function on , where the moments appear as the derivatives at 0. As an application, we calculate the moments of the Kerr solution. We also discuss the freedom in choosing the potential for the moments.
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| 18. |
- Bäckdahl, Thomas, 1980-
(författare)
-
Multipole moments of axisymmetric spacetimes
- 2006
-
Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis we study multipole moments of axisymmetric spacetimes. Using the recursive definition of the multipole moments of Geroch and Hansen we develop a method for computing all multipole moments of a stationary axisymmetric spacetime without the use of a recursion. This is a generalisation of a method developed by Herberthson for the static case.Using Herberthson’s method we also develop a method for finding a static axisymmetric spacetime with arbitrary prescribed multipole moments, subject to a specified convergence criteria. This method has, in general, a step where one has to find an explicit expression for an implicitly defined function. However, if the number of multipole moments are finite we give an explicit expression in terms of power series.
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| 19. |
- Bäckdahl, Thomas, 1980-
(författare)
-
Multipole Moments of Stationary Spacetimes
- 2008
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis we study the relativistic multipole moments for stationary asymptotically flat spacetimes as introduced by Geroch and Hansen. These multipole moments give an asymptotic description of the gravitational field in a coordinate independent way.Due to this good description of the spacetimes, it is natural to try to construct a spacetime from only the set of multipole moments. Here we present a simple method to do this for the static axisymmetric case. We also give explicit solutions for the cases where the number of non-zero multipole moments are finite. In addition, for the general stationary axisymmetric case, we present methods to generate solutions.It has been a long standing conjecture that the multipole moments give a complete characterization of the stationary spacetimes. Much progress toward a proof has been made over the years. However, there is one remaining difficult task: to prove that a spacetime exists with an a-priori given arbitrary set of multipole moments subject to some given condition.Here we present such a condition for the axisymmetric case, and prove that it is both necessary and sufficient. We also extend this condition to the general case without axisymmetry, but in this case we only prove the necessity of our condition.
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| 20. |
- Bäckdahl, Thomas, et al.
(författare)
-
Static axisymmetric spacetimes with prescribed multipole moments
- 2005
-
Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 22:9, s. 1607-1621
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper we develop a method of finding the static axisymmetric spacetime corresponding to any given set ofmultipolemoments. In addition to an implicit algebraic form for the general solution, we also give a power series expression for all finite sets of multipole moments. As conjectured by Geroch we prove in the special case of axisymmetry, that there is a static spacetime for any given set of multipole moments subject to a (specified) convergence criterion. We also use this method to confirm a conjecture of Hernández-Pastora and Martín concerning the monopole–quadrupole solution.
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| 21. |
- Herberthson, Magnus
(författare)
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A C-> 1 completion of the Kerr space-time at spacelike infinity including I+ and I-
- 2001
-
Ingår i: General Relativity and Gravitation. - 0001-7701 .- 1572-9532. ; 33:7, s. 1197-1205
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Tidskriftsartikel (refereegranskat)abstract
- It is well known that, for asymptotically flat spacetimes, one cannot in general have a smooth differentiable structure at spacelike infinity, i(0). Normally, one uses direction dependent structures, whose regularity has to match the regularity of the (rescaled) metric. The standard C->1-structure at i(0) ensures sufficient regularity in spacelike directions, but examples show very low regularity on I+ and I-. The alternative C1+-structure shows that both null and spacelike directions may be treated on an equal footing, at the expense of some manageable logarithmic singularities at i(0). In this paper, we show that the Kerr spacetime may be rescaled and given a structure which is C->1 in both null and spacelike directions from i(0).
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| 22. |
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| 23. |
- Herberthson, Magnus
(författare)
-
Bounds for, and calculation of, the multipole moments of stationary spacetimes
- 2007
-
Ingår i: Journal of Physics, Conference Series. - : IOP Publishing. - 1742-6588 .- 1742-6596. ; 66:1
-
Tidskriftsartikel (refereegranskat)abstract
- The multipole moments of stationary asymptotically flat spacetimes are considered. We demostrate how the tensorial recursion of Geroch and Hansen can be replaced by a scalar recursion on R2. We also give a bound on multipole moments. This confirms the "necessary part" of a long standing conjecture due to Geroch. © 2007 IOP Publishing Ltd.
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| 24. |
- Herberthson, Magnus, et al.
(författare)
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Dynamics of local magnetization in the eigenbasis of the Bloch-Torrey operator
- 2017
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Ingår i: Journal of Chemical Physics. - : AMER INST PHYSICS. - 0021-9606 .- 1089-7690. ; 146:12
-
Tidskriftsartikel (refereegranskat)abstract
- We consider diffusion within pores with general shapes in the presence of spatially linear magnetic field profiles. The evolution of local magnetization of the spin bearing particles can be described by the Bloch-Torrey equation. We study the diffusive process in the eigenbasis of the non-Hermitian Bloch-Torrey operator. It is possible to find expressions for some special temporal gradient waveforms employed to sensitize the nuclear magnetic resonance (NMR) signal to diffusion. For more general gradient waveforms, we derive an efficient numerical solution by introducing a novel matrix formalism. Compared to previous methods, this new approach requires a fewer number of eigenfunctions to achieve the same accuracy. This shows that these basis functions are better suited to the problem studied. The new framework could provide new important insights into the fundamentals of diffusion sensitization, which could further the development of the field of NMR. Published by AIP Publishing.
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| 25. |
- Herberthson, Magnus, 1963-
(författare)
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EM Scattering Calculations using Potentials
- 2010
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Ingår i: Scientific Computing in Electrical Engineering, SCEE 2008. - Berlin, Heidelberg : Springer Berlin/Heidelberg. - 9783642122934 ; , s. 171-172
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- EM scattering from PEC surfaces are mostly calculated through the induced surface current J. In this paper, we consider PEC surfaces homeomorphic to the sphere, apply Hodge decomposition theorem to a slightly rewritten surface current, and show how this enables us to replace the unknown current with two scalar functions which serve as potentials for the current. Implications of this decomposition are pointed out, and numerical results are demonstrated.
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| 26. |
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| 27. |
- Herberthson, Magnus, et al.
(författare)
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Orientationally-averaged diffusion-attenuated magnetic resonance signal for locally-anisotropic diffusion
- 2019
-
Ingår i: Scientific Reports. - : NATURE PUBLISHING GROUP. - 2045-2322. ; 9
-
Tidskriftsartikel (refereegranskat)abstract
- Diffusion-attenuated MR signal for heterogeneous media has been represented as a sum of signals from anisotropic Gaussian sub-domains to the extent that this approximation is permissible. Any effect of macroscopic (global or ensemble) anisotropy in the signal can be removed by averaging the signal values obtained by differently oriented experimental schemes. The resulting average signal is identical to what one would get if the micro-domains are isotropically (e.g., randomly) distributed with respect to orientation, which is the case for "powdered" specimens. We provide exact expressions for the orientationally-averaged signal obtained via general gradient waveforms when the microdomains are characterized by a general diffusion tensor possibly featuring three distinct eigenvalues. This extends earlier results which covered only axisymmetric diffusion as well as measurement tensors. Our results are expected to be useful in not only multidimensional diffusion MR but also solid-state NMR spectroscopy due to the mathematical similarities in the two fields.
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| 28. |
- Herberthson, Magnus, 1963-, et al.
(författare)
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P-averages of diffusion tensors
- 2007
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Ingår i: SSBA 2007, Symposium on image analysis,2007. - Linköping.
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- For positive semi-definite tensors like diffusion tensors in the plane it is possible to calculate several different means or p-averages. These are related to p-norms for functions, but produce mappings rather than numbers as means. We compare these means for various values of the real parameter p. One important future application is the filtering and interpolation of tensor fields in Diffusion Tensor Magnetic Resonance
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| 29. |
- Herberthson, Magnus, 1963-, et al.
(författare)
-
Pairs of orientation in the plane
- 2006
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Ingår i: SSBA Symposium on Image Analysis,2006. ; , s. 97-100
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)
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| 30. |
- Herberthson, Magnus, et al.
(författare)
-
Q-space trajectory imaging with positivity constraints (QTI plus )
- 2021
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Ingår i: NeuroImage. - : Elsevier. - 1053-8119 .- 1095-9572. ; 238
-
Tidskriftsartikel (refereegranskat)abstract
- Q-space trajectory imaging (QTI) enables the estimation of useful scalar measures indicative of the local tissue structure. This is accomplished by employing generalized gradient waveforms for diffusion sensitization alongside a diffusion tensor distribution (DTD) model. The first two moments of the underlying DTD are made available by acquisitions at low diffusion sensitivity (b-values). Here, we show that three independent conditions have to be fulfilled by the mean and covariance tensors associated with distributions of symmetric positive semidefinite tensors. We introduce an estimation framework utilizing semi-definite programming (SDP) to guarantee that these conditions are met. Applying the framework on simulated signal profiles for diffusion tensors distributed according to non-central Wishart distributions demonstrates the improved noise resilience of QTI+ over the commonly employed estimation methods. Our findings on a human brain data set also reveal pronounced improvements, especially so for acquisition protocols featuring few number of volumes. Our methods robustness to noise is expected to not only improve the accuracy of the estimates, but also enable a meaningful interpretation of contrast in the derived scalar maps. The techniques performance on shorter acquisitions could make it feasible in routine clinical practice.
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| 31. |
- Herberthson, Magnus, 1963-, et al.
(författare)
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Representing Pairs of Orientations in the Plane
- 2007
-
Ingår i: Image Analysis. - Berlin, Heidelberg : Springer Berlin/Heidelberg. - 9783540730392 - 9783540730408 ; , s. 661-670
-
Konferensbidrag (refereegranskat)abstract
- In this article we present a way of representing pairs of orientations in the plane. This is an extension of the familiar way of representing single orientations in the plane. Using this framework, pairs of lines can be added, scaled and averaged over in a sense which is to be described. In particular, single lines can be incorporated and handled simultaneously.
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| 32. |
- Herberthson, Magnus, 1963-
(författare)
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Static spacetimes with prescribed multipole moments: a proof of a conjecture by Geroch
- 2009
-
Ingår i: Classical and quantum gravity. - Bristol, UK : IOP Publishing. - 0264-9381 .- 1361-6382. ; 26:21, s. 1-26
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper we give sufficient conditions on a sequence of multipole moments for a static spacetime to exist with precisely these moments. The proof is constructive in the sense that a metric having prescribed multipole moments up to a given order can be calculated. Since these sufficient conditions agree with already known necessary conditions, this completes the proof of a long standing conjecture due to Geroch.
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| 33. |
- Herberthson, Magnus
(författare)
-
Static vacuum spacetimes with prescribed multipole moments
- 2010
-
Ingår i: Journal of Physics, Conference Series. - : IOP Publishing. - 1742-6588 .- 1742-6596. ; 229
-
Tidskriftsartikel (refereegranskat)abstract
- This paper gives sufficient conditions on a sequence of multipole moments for a static spacetime to exist with precisely these moments. We outline the proof, which is constructive in the sense that a metric having prescribed multipole moments up to a given order can be calculated. These sufficient conditions agree with already known necessary conditions, and hence this completes the proof of a long standing conjecture due to Geroch
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| 34. |
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| 35. |
- Herberthson, Magnus, 1963-
(författare)
-
The gravitational dipole and explicit multipole moments of static axisymmetric spacetimes
- 2004
-
Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 21:22, s. 5121-5138
-
Tidskriftsartikel (refereegranskat)abstract
- The multipole moments of static axisymmetric asymptotically flat spacetimes are considered. The usual set of recursively defined tensors is replaced with one real-valued function m defined on R+ ∪ {0}, where the moments are given by the derivatives of m at 0. As examples of applications, we show that the Schwarzschild spacetime is the gravitational monopole and derive the metric for the gravitational dipole.
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| 36. |
- Herberthson, Magnus, 1963-
(författare)
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The potential method for scattering calculations
- 2007
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Ingår i: Swedish National Conference on Computational Electromagnetics, EMB 07,2007. - Lund : EMB 07. ; , s. 225-
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Konferensbidrag (refereegranskat)
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| 37. |
- Knutsson, Hans, et al.
(författare)
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An Iterated Complex Matrix Approach for Simulation and Analysis of Diffusion MRI Processes
- 2015
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Ingår i: MEDICAL IMAGE COMPUTING AND COMPUTER-ASSISTED INTERVENTION - MICCAI 2015, PT I. - Cham : SPRINGER INT PUBLISHING AG. - 9783319245539 - 9783319245522 ; , s. 61-68
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Konferensbidrag (refereegranskat)abstract
- We present a novel approach to investigate the properties of diffusion weighted magnetic resonance imaging (dMRI). The process of restricted diffusion of spin particles in the presence of a magnetic field is simulated by an iterated complex matrix multiplication approach. The approach is based on first principles and provides a flexible, transparent and fast simulation tool. The experiments carried out reveals fundamental features of the dMRI process. A particularly interesting observation is that the induced speed of the local spatial spin angle rate of change is highly shift variant. Hence, the encoding basis functions are not the complex exponentials associated with the Fourier transform as commonly assumed. Thus, reconstructing the signal using the inverse Fourier transform leads to large compartment estimation errors, which is demonstrated in a number of 1D and 2D examples. In accordance with previous investigations the compartment size is under-estimated. More interestingly, however, we show that the estimated shape is likely to be far from the true shape using state of the art clinical MRI scanners.
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| 38. |
- Ordinola, Alfredo Miguel, et al.
(författare)
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Limitations and generalizations of the first order kinetics reaction expression for modeling diffusion-driven exchange: Implications on NMR exchange measurements
- 2024
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 160:8
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Tidskriftsartikel (refereegranskat)abstract
- The study and modeling of water exchange in complex media using different applications of diffusion and relaxation magnetic resonance (MR) have been of interest in recent years. Most models attempt to describe this process using a first order kinetics expression, which is appropriate to describe chemical exchange; however, it may not be suitable to describe diffusion-driven exchange since it has no direct relationship to diffusion dynamics of water molecules. In this paper, these limitations are addressed through a more general exchange expression that does consider such important properties. This exchange fraction expression features a multi-exponential recovery at short times and a mono-exponential decay at long times, both of which are not captured by the first order kinetics expression. Furthermore, simplified exchange expressions containing partial information of the analyzed system's diffusion and relaxation processes and geometry are proposed, which can potentially be employed in already established estimation protocols. Finally, exchange fractions estimated from simulated MR data and derived here were compared, showing qualitative similarities but quantitative differences, suggesting that the features of the derived exchange fraction in this paper can be partially recovered by employing an existing estimation framework.
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| 39. |
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| 40. |
- Sjölund, Jens, 1987-, et al.
(författare)
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Bayesian uncertainty quantification in linear models for diffusion MRI
- 2018
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Ingår i: NeuroImage. - : Elsevier BV. - 1053-8119 .- 1095-9572. ; 175, s. 272-285
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Tidskriftsartikel (refereegranskat)abstract
- Diffusion MRI (dMRI) is a valuable tool in the assessment of tissue microstructure. By fitting a model to the dMRI signal it is possible to derive various quantitative features. Several of the most popular dMRI signal models are expansions in an appropriately chosen basis, where the coefficients are determined using some variation of least-squares. However, such approaches lack any notion of uncertainty, which could be valuable in e.g. group analyses. In this work, we use a probabilistic interpretation of linear least-squares methods to recast popular dMRI models as Bayesian ones. This makes it possible to quantify the uncertainty of any derived quantity. In particular, for quantities that are affine functions of the coefficients, the posterior distribution can be expressed in closed-form. We simulated measurements from single- and double-tensor models where the correct values of several quantities are known, to validate that the theoretically derived quantiles agree with those observed empirically. We included results from residual bootstrap for comparison and found good agreement. The validation employed several different models: Diffusion Tensor Imaging (DTI), Mean Apparent Propagator MRI (MAP-MRI) and Constrained Spherical Deconvolution (CSD). We also used in vivo data to visualize maps of quantitative features and corresponding uncertainties, and to show how our approach can be used in a group analysis to downweight subjects with high uncertainty. In summary, we convert successful linear models for dMRI signal estimation to probabilistic models, capable of accurate uncertainty quantification. © 2018 Elsevier Inc.
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| 41. |
- Yolcu, Cem, et al.
(författare)
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Magnetic resonance assessment of effective confinement anisotropy with orientationally-averaged single and double diffusion encoding
- 2021
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Ingår i: Anisotropy across fields and scales. - Cham : Springer. - 9783030562144 - 9783030562151 ; , s. 203-223
-
Bokkapitel (refereegranskat)abstract
- Porous or biological materials comprise a multitude of micro-domainscontaining water. Diffusion-weighted magnetic resonance measurements are sensitive to the anisotropy of the thermal motion of such water. This anisotropy can bedue to the domain shape, as well as the (lack of) dispersion in their orientations.Averaging over measurements that span all orientations is a trick to suppress thelatter, thereby untangling it from the influence of the domains’ anisotropy on thesignal. Here, we consider domains whose anisotropy is modeled as being the resultof a Hookean (spring) force, which has the advantage of having a Gaussian diffusionpropagator while still confining the spatial range for the diffusing particles. In fact,this confinement model is the effective model of restricted diffusion when diffusion isencoded via gradients of long durations, making the model relevant to a broad rangeof studies aiming to characterize porous media with microscopic subdomains. In thisstudy, analytical expressions for the powder-averaged signal under this assumptionare given for so-called single and double diffusion encoding schemes, which sensitize the MR signal to the diffusive displacement of particles in, respectively, one ortwo consecutive time intervals. The signal for one-dimensional diffusion is shownto exhibit power-law dependence on the gradient strength while its coefficient bearssignatures of restricted diffusion.
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| 42. |
- Özarslan, Evren, et al.
(författare)
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Diffusion within pores fully revealed by magnetic resonance
- 2023
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 158:16
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Tidskriftsartikel (refereegranskat)abstract
- The diffusion propagator fully characterizes the diffusion process, which is highly sensitive to the confining boundaries and the structure within enclosed pores. While magnetic resonance has extensively been used to observe various features of the diffusion process, its full characterization has been elusive. Here, we address this challenge by employing a special sequence of magnetic field gradient pulses for measuring the diffusion propagator, which allows for "listening to the drum," mapping structural dispersity, and determining not only the pores shape but also diffusive dynamics within it.
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| 43. |
- Özarslan, Evren, 1976-, et al.
(författare)
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Effective Potential for Magnetic Resonance Measurements of Restricted Diffusion
- 2017
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Ingår i: Frontiers in Physics. - : Frontiers Media S.A.. - 2296-424X. ; 5
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Tidskriftsartikel (refereegranskat)abstract
- The signature of diffusive motion on the NMR signal has been exploited to characterize the mesoscopic structure of specimens in numerous applications. For compartmentalized specimens comprising isolated subdomains, a representation of individual pores is necessary for describing restricted diffusion within them. When gradient waveforms with long pulse durations are employed, a quadratic potential profile is identified as an effective energy landscape for restricted diffusion. The dependence of the stochastic effective force on the center-of-mass position is indeed found to be approximately linear (Hookean) for restricted diffusion even when the walls are sticky. We outline the theoretical basis and practical advantages of our picture involving effective potentials.
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| 44. |
- Özarslan, Evren, 1976-, et al.
(författare)
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Influence of the Size and Curvedness of Neural Projections on the Orientationally Averaged Diffusion MR Signal
- 2018
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Ingår i: Frontiers in Physics. - : Frontiers Media S.A.. - 2296-424X. ; 6, s. 1-10
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Tidskriftsartikel (refereegranskat)abstract
- Neuronal and glial projections can be envisioned to be tubes of infinitesimal diameter as far as diffusion magnetic resonance (MR) measurements via clinical scanners are concerned. Recent experimental studies indicate that the decay of the orientationally-averaged signal in white-matter may be characterized by the power-law, Ē(q) ∝ q−1, where q is the wavenumber determined by the parameters of the pulsed field gradient measurements. One particular study by McKinnon et al. [1] reports a distinctively faster decay in gray-matter. Here, we assess the role of the size and curvature of the neurites and glial arborizations in these experimental findings. To this end, we studied the signal decay for diffusion along general curves at all three temporal regimes of the traditional pulsed field gradient measurements. We show that for curvy projections, employment of longer pulse durations leads to a disappearance of the q−1 decay, while such decay is robust when narrow gradient pulses are used. Thus, in clinical acquisitions, the lack of such a decay for a fibrous specimen can be seen as indicative of fibers that are curved. We note that the above discussion is valid for an intermediate range of q-values as the true asymptotic behavior of the signal decay is Ē(q) ∝ q−4 for narrow pulses (through Debye-Porod law) or steeper for longer pulses. This study is expected to provide insights for interpreting the diffusion-weighted images of the central nervous system and aid in the design of acquisition strategies.
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