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Bjørn Jensen

Publications and source records attributed to Bjørn Jensen.

15 recordsLinked to original sources
arXiv2025

Dual-grid parameter choice method with application to image deblurring

Variational regularization of ill-posed inverse problems is based on minimizing the sum of a data fidelity term and a regularization term. The balance between them is tuned using a positive regularization parameter, whose automatic choice remains an open question in general. A novel approach for parameter choice is introduced, based on the use of two slightly different computational models for the same inverse problem. Small parameter values should give two very different reconstructions due to amplification of noise. Large parameter values lead to two identical but trivial reconstructions. Optimal parameter is chosen between the extremes by matching image similarity of the two reconstructions with a pre-defined value. Efficacy of the new method is demonstrated with image deblurring using measured data and two different regularizers.

math.NA↗
arXiv2024

A nonsmooth primal-dual method with interwoven PDE constraint solver

We introduce an efficient first-order primal-dual method for the solution of nonsmooth PDE-constrained optimization problems. We achieve this efficiency through not solving the PDE or its linearisation on each iteration of the optimization method. Instead, we run the method interwoven with a simple conventional linear system solver (Jacobi, Gauss-Seidel, conjugate gradients), always taking only one step of the linear system solver for each step of the optimization method. The control parameter is updated on each iteration as determined by the optimization method. We prove linear convergence under a second-order growth condition, and numerically demonstrate the performance on a variety of PDEs related to inverse problems involving boundary measurements.

math.OC↗
arXiv2024

Feasibility of Acousto-Electric Tomography

In acousto-electric tomography the goal is to reconstruct the electric conductivity in a domain from electrostatic boundary measurements of corresponding currents and voltages, while the domain is penetrated by a time-dependent acoustic wave. We explicitly model the phenomena, and we propose a complete inversion framework for acousto-electric tomography in two steps: First the interior power density is obtained from boundary measurements by solving a linear, ill-posed problem; second the interior conductivity is reconstructed from the power density by solving a non-linear, fairly well-posed problem. We perform numerical experiments on synthetic data with realistically chosen parameters. We investigate how feasibility of reconstructing the electrical conductivity from boundary measurements depends on the acousto-electric coupling constant and measurement noise. Our findings are positive, and indicate that AET is indeed feasible for interesting applications in for example medical imaging. Finally, we consider a limited angle setup and show that the conductivity is well reconstructed near the measurement boundary.

physics.med-ph↗
arXiv2022

Conductivity reconstruction from power density data in limited view

In Acousto-Electric tomography, the objective is to extract information about the interior electrical conductivity in a physical body from knowledge of the interior power density data generated from prescribed boundary conditions for the governing elliptic partial differential equation. In this note, we consider the problem when the controlled boundary conditions are applied only on a small subset of the full boundary. We demonstrate using the unique continuation principle that the Runge approximation property is valid also for this special case of limited view data. As a consequence, we guarantee the existence of finitely many boundary conditions such that the corresponding solutions locally satisfy a non-vanishing gradient condition. This condition is essential for conductivity reconstruction from power density data. In addition, we adapt an existing reconstruction method intended for the full data situation to our setting. We implement the method numerically and investigate the opportunities and shortcomings when reconstructing from two fixed boundary conditions.

math.AP↗
arXiv2021

Efficient Uncertainty Quantification and Sensitivity Analysis in Epidemic Modelling using Polynomial Chaos

In the political decision process and control of COVID-19 (and other epidemic diseases), mathematical models play an important role. It is crucial to understand and quantify the uncertainty in models and their predictions in order to take the right decisions and trustfully communicate results and limitations. We propose to do uncertainty quantification in SIR-type models using the efficient framework of generalized Polynomial Chaos. Through two particular case studies based on Danish data for the spread of Covid-19 we demonstrate the applicability of the technique. The test cases are related to peak time estimation and superspeading and illustrate how very few model evaluations can provide insightful statistics.

stat.AP↗
arXiv2018

Acousto-Electric Tomography with Total Variation Regularization

We study the numerical reconstruction problem in acousto-electric tomography of recovering the conductivity distribution in a bounded domain from interior power density data. We propose a numerical method for recovering discontinuous conductivity distributions, by reformulating it as an optimization problem with $ L^1 $ fitting and total variation penalty subject to PDE constraints. We establish continuity and differentiability results for the forward map, the well-posedness of the optimization problem, and present an easy-to-implement and robust numerical method based on successive linearization, smoothing and iterative reweighing. Extensive numerical experiments are presented to illustrate the feasibility of the proposed approach.

math.OC↗
arXiv2018

On the Sagnac effect and Quantum Mechanics in a Rotating Reference System

We canonically quantize a spin-less non-relativistic point particle in a rigidly rotating cylinder symmetric reference system. The resulting quantum mechanics is investigated in the case of both a two-dimensional cylindrical shell and in the case of the full rotating cylinder; in both cases energy eigenstates exist which exhibit rotation induced negative energies. Based on a reanalysis of the classical Sagnac effect a novel way to compute the quantum Sagnac phase shift is deduced. It is pointed out that certain states on both the cylindrical shell and in the bulk give rise to a novel anomalous quantum Sagnac effect.

quant-ph↗
arXiv1997

On the Stability of the GPS Magnetic Monopole Solution

The question of the stability of the four dimensional Gross-Perry-Sorkin Kaluza-Klein magnetic monopole solution is investigated within the framework of a N=2, D=5 supergravity theory. We show that this solution does not support a spin structure of the Killing type and is therefore, contrary to previous expectations, not necessarily stable.

hep-th↗
arXiv1996

Classical Interactions for Tensionless Strings

Using an ``action at a distance'' formulation we probe the possible classical interactions for tensionless strings, (the $T\to 0$ limit of the ordinary bosonic string.) We find $G_{μν}$ and $B_{μν}$ type interactions but no dilaton interactions.

hep-th↗
arXiv1996

The Number of Particles Released in Gauge Cosmic String Formation

We give a simple derivation of a new formal expression for the number of particles produced from a conformal scalar field vacuum due to the creation of a gauge cosmic string. We find that the number of particles released in string formation may be substantially lower than what previous estimates have indicated. Our derivation also indicates that there always exists at least one critical angle deficit less than $2π$, at which the particle production attains a maximum value. At the end we argue that additional (quantum) effects will occur in string formation. In particular, a new mechanism to produce small scale structure on strings is proposed.

hep-th↗
arXiv1996

A stringy black string and a stringy black hole in four dimensions

We uplift the static three dimensional black hole solution found by Banados, Teitelboim and Zanelli (BTZ) into four dimensional space time. In this way we obtain a black string solution with a relativistic string source, as well as a new black hole solution which is also generated by a relativistic ``stringy'' source. It is shown that when passing continuously from the region of the one dimensional parameter spaces which characterize these solutions, containing naked singular strings or naked singular ``points'', and into the region containing black strings or black holes, the metrics ``blow up'' at a critical point in both parameter spaces. We show that a similar ``separation'' mechanism can be introduced in three dimensions. In this way we also obtain a generalization of the BTZ solution. The ``separation'' mechanism, and its immediate consequences, offers an hitherto missing technical argument needed in order to exclude the naked singularities (the ``mass gap'') from the space of ``physically permissible'' solutions in three dimensional Einstein theory coupled to a negative cosmological constant. PACS nos.: 04.40.Nr, 04.20.Cv

gr-qc↗
arXiv1996

Anisotropic domain walls

We find an anisotropic, non-supersymmetric generalization of the extreme supersymmetric domain walls of simple non-dilatonic supergravity theory. As opposed to the isotropic non- and ultra-extreme domain walls, the anisotropic non-extreme wall has the \emph{same} spatial topology as the extreme wall. The solution has naked singularities which vanish in the extreme limit. Since the Hawking temperature on the two sides is different, the generic solution is unstable to Hawking decay.

gr-qc↗
arXiv1995

Rotating Dilaton Black Holes

We consider the axially symmetric coupled system of gravitation, electromagnetism and a dilaton field. Reducing from four to three dimensions, the system is described by gravity coupled to a non-linear $σ$-model. We find the target space isometries and use them to generate new solutions. It seems that it is only possible to generate rotating solutions from non-rotating ones for the special cases when the dilaton coupling parameter $a=0, \pm \sqrt{3}$. For those particular values, the target space symmetry is enlarged.

gr-qc↗
arXiv1994

Aspects of the Thermo-Dynamics of a Black Hole with a Topological Defect

Aspects of the thermo-dynamics of a black hole which is either pierced by a cosmic gauge string or contains a global monopole are investigated. We also make some comments on the physical significance of the fact that the gravitational mass carried by a global monopole is negative. We note in particular that the negative monopole mass implies a gravitational super-radiance effect.

gr-qc↗