| 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
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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
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Ingår i: International Journal of Geometric Methods in Modern Physics (IJGMMP). - 0219-8878. ; 2:1, s. 13-21
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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
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Ingår i: SoftwareX. - : Elsevier. - 2352-7110. ; 18
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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
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Ingår i: Magnetic Resonance Letters. - : KeAi Publishing Communications. - 2772-5162. ; 3:2, s. 187-196
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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
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Ingår i: Image Analysis. - Berlin, Heidelberg : Springer Berlin/Heidelberg. - 9783540263203 - 9783540315667 ; , s. 920-
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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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