Stray Magnetic Field Compensation with a Scalar Atomic Magnetometer

We describe a system for the compensation of time-dependent stray magnetic fields using a dual channel scalar magnetometer based on non-linear Faraday rotation in synchronously optically pumped Cs vapour. We detail the active control strategy, with an emphasis on the electronic circuitry, based on a simple phase-locked-loop integrated circuit. The performance and limits of the system developed are tested and discussed. The system was applied to significantly improve the detection of free induction decay signals from protons of remotely magnetized water precessing in an ultra-low magnetic field.Comment: 8 pages, 6 figures, 31 refs, v2 (with minor improvements) appearing in Rev.Sc.Instr. June 201

A Primal-Dual Proximal Algorithm for Sparse Template-Based Adaptive Filtering: Application to Seismic Multiple Removal

Unveiling meaningful geophysical information from seismic data requires to deal with both random and structured "noises". As their amplitude may be greater than signals of interest (primaries), additional prior information is especially important in performing efficient signal separation. We address here the problem of multiple reflections, caused by wave-field bouncing between layers. Since only approximate models of these phenomena are available, we propose a flexible framework for time-varying adaptive filtering of seismic signals, using sparse representations, based on inaccurate templates. We recast the joint estimation of adaptive filters and primaries in a new convex variational formulation. This approach allows us to incorporate plausible knowledge about noise statistics, data sparsity and slow filter variation in parsimony-promoting wavelet frames. The designed primal-dual algorithm solves a constrained minimization problem that alleviates standard regularization issues in finding hyperparameters. The approach demonstrates significantly good performance in low signal-to-noise ratio conditions, both for simulated and real field seismic data

A spectral scheme for Kohn-Sham density functional theory of clusters

Starting from the observation that one of the most successful methods for solving the Kohn-Sham equations for periodic systems -- the plane-wave method -- is a spectral method based on eigenfunction expansion, we formulate a spectral method designed towards solving the Kohn-Sham equations for clusters. This allows for efficient calculation of the electronic structure of clusters (and molecules) with high accuracy and systematic convergence properties without the need for any artificial periodicity. The basis functions in this method form a complete orthonormal set and are expressible in terms of spherical harmonics and spherical Bessel functions. Computation of the occupied eigenstates of the discretized Kohn-Sham Hamiltonian is carried out using a combination of preconditioned block eigensolvers and Chebyshev polynomial filter accelerated subspace iterations. Several algorithmic and computational aspects of the method, including computation of the electrostatics terms and parallelization are discussed. We have implemented these methods and algorithms into an efficient and reliable package called ClusterES (Cluster Electronic Structure). A variety of benchmark calculations employing local and non-local pseudopotentials are carried out using our package and the results are compared to the literature. Convergence properties of the basis set are discussed through numerical examples. Computations involving large systems that contain thousands of electrons are demonstrated to highlight the efficacy of our methodology. The use of our method to study clusters with arbitrary point group symmetries is briefly discussed.Comment: Manuscript submitted (with revisions) to Journal of Computational Physic

On-line reconstruction algorithms for the CBM and ALICE experiments

Diese Dissertation präsentiert verschiedenen Algorithmen, die für die Echtzeit-Ereignisrekonstruktion im CBM-Experiment der GSI (in Darmstadt) und im ALICE-Experiment am CERN (in Genf) entwickelt wurden. Obwohl diese Experimente unterschiedlich sind - CBM ist ein Fixed-Target Experiment mit Forward-Geometrie, während ALICE eine typische Collider-Geometrie hat - gibt es bei der Rekonstruktion gemeinsame Aspekte. Diese Arbeit beschreibt: — allgemeine Änderungen an der Kalman-Filter-Methode, die bestehende Fit-Algorithmen (auch Anpassungsalgorithmen genannt) beschleunigen, vereinfachen sowie deren numerische Stabilität verbessern. — Fit-Algorithmen, die für die CBM und ALICE Experimente entwickelt wurden, inklusive einer neuen Methode für die Spurextrapolation in nicht-homogenen Magnetfeldern. — die entwickelten Algorithmen für die Bestimmung der primären und sekundären Vertices in beiden Experimenten. Insbesondere wird eine Methode zur Rekonstruktion der zerfallenen Teilchen vorgestellt. — parallelisierte Methoden für die Echtzeit-Spursuche im CBM Experiment. — parallelisierte Methoden zur Echtzeit-Spursuche im High Level Trigger des ALICE-Experiments. — die Realisierung der Spurrekonsturtion auf moderner Hardware, insbesondere Vektorprozessoren und GPUs. Alle vorgestellten Methoden sind vom oder mit direkter Beteiligung des Autors entwickelt worden.This thesis presents various algorithms which have been developed for on-line event reconstruction in the CBM experiment at GSI, Darmstadt and the ALICE experiment at CERN, Geneve. Despite the fact that the experiments are different — CBM is a fixed target experiment with forward geometry, while ALICE has a typical collider geometry — they share common aspects when reconstruction is concerned. The thesis describes: — general modifications to the Kalman filter method, which allows one to accelerate, to improve, and to simplify existing fit algorithms; — developed algorithms for track fit in CBM and ALICE experiment, including a new method for track extrapolation in non-homogeneous magnetic field. — developed algorithms for primary and secondary vertex fit in the both experiments. In particular, a new method of reconstruction of decayed particles is presented. — developed parallel algorithm for the on-line tracking in the CBM experiment. — developed parallel algorithm for the on-line tracking in High Level Trigger of the ALICE experiment. — the realisation of the track finders on modern hardware, such as SIMD CPU registers and GPU accelerators. All the presented methods have been developed by or with the direct participation of the author

Non-parametric PSF estimation from celestial transit solar images using blind deconvolution

Context: Characterization of instrumental effects in astronomical imaging is important in order to extract accurate physical information from the observations. The measured image in a real optical instrument is usually represented by the convolution of an ideal image with a Point Spread Function (PSF). Additionally, the image acquisition process is also contaminated by other sources of noise (read-out, photon-counting). The problem of estimating both the PSF and a denoised image is called blind deconvolution and is ill-posed. Aims: We propose a blind deconvolution scheme that relies on image regularization. Contrarily to most methods presented in the literature, our method does not assume a parametric model of the PSF and can thus be applied to any telescope. Methods: Our scheme uses a wavelet analysis prior model on the image and weak assumptions on the PSF. We use observations from a celestial transit, where the occulting body can be assumed to be a black disk. These constraints allow us to retain meaningful solutions for the filter and the image, eliminating trivial, translated and interchanged solutions. Under an additive Gaussian noise assumption, they also enforce noise canceling and avoid reconstruction artifacts by promoting the whiteness of the residual between the blurred observations and the cleaned data. Results: Our method is applied to synthetic and experimental data. The PSF is estimated for the SECCHI/EUVI instrument using the 2007 Lunar transit, and for SDO/AIA using the 2012 Venus transit. Results show that the proposed non-parametric blind deconvolution method is able to estimate the core of the PSF with a similar quality to parametric methods proposed in the literature. We also show that, if these parametric estimations are incorporated in the acquisition model, the resulting PSF outperforms both the parametric and non-parametric methods.Comment: 31 pages, 47 figure

Laplacian Projection Based Global Physical Prior Smoke Reconstruction

We present a novel framework for reconstructing fluid dynamics in real-life scenarios. Our approach leverages sparse view images and incorporates physical priors across long series of frames, resulting in reconstructed fluids with enhanced physical consistency. Unlike previous methods, we utilize a differentiable fluid simulator (DFS) and a differentiable renderer (DR) to exploit global physical priors, reducing reconstruction errors without the need for manual regularization coefficients. We introduce divergence-free Laplacian eigenfunctions (div-free LE) as velocity bases, improving computational efficiency and memory usage. By employing gradient-related strategies, we achieve better convergence and superior results. Extensive experiments demonstrate the effectiveness of our method, showcasing improved reconstruction quality and computational efficiency compared to existing approaches. We validate our approach using both synthetic and real data, highlighting its practical potential

Long-run exchange rate determination: A neural network study

Foreign Exchange;Exchange Rate;Econometrics;Neural Network

Analysis and Mitigation of the Effect of Magnetic Field Inhomogeneities and Undersampling Artifacts on Magnetic Resonance Fingerprinting

Magnetic resonance imaging (MRI) is largely limited to producing qualitative contrast images instead of quantitative maps of tissue characteristics. A novel framework for quantitative MRI termed Magnetic Resonance Fingerprinting (MRF) to map tissue parameters such as the relaxation times T1 and T2 has recently been introduced. In MRF, tissue signals are generated by applying a pseudo-randomly varying MRI acquisition, acquired using highly undersampled trajectories and matched to a database of simulated tissue signals. The aim of this thesis is to investigate hypotheses underlying MRF regarding its susceptibility to undersampling artifacts and magnetic field inhomogeneities and develop countermeasures. Since MRF can be implemented in various ways, one of the most popular implementations based on the FISP (Fast Imaging with Steady State Precession) sequence was chosen for analysis and as a basis for further developments. The single shot spiral trajectories employed lead to substantial undersampling artifacts. In this work, the temporal variation of the spiral sampling patterns was examined and optimized. The results show that the originally proposed temporal order yields artifacts of similar frequencies as the signal responses from tissues, which leads to spatially dependent misestimations of parameters. To resolve those, an optimized temporal order was developed in simulations and proven in in-vivo experiments. The following chapter is dedicated to the influence of magnetic field inhomogeneities on MRF. Here it is shown that different local amplitudes of the radio frequency (RF) field B1+ can lead to misestimations of parameters by up to 50%, which can be resolved by measuring a B1+ map and integrating the information in the pattern match. Another newly developed strategy in this work is to mitigate the influence of B1+ by the introduction of acquisition segments that are particularly sensitive to B1+. Two approaches were developed and evaluated, one including FLASH (Fast Low-Angle Shot) and one using two 90° phase shifted pulses. Here, tissue parameter maps and B1+ maps were simultaneously generated, thereby resolving interdependencies. Furthermore, in this work it was found that the static magnetic field B0 can also have an impact on FISP-MRF. The dependency was analyzed and related to the relative phase difference between spin ensembles and RF pulses. A technique to mitigate the dependency by additionally dephasing spins before RF pulses was developed. The chapter is concluded with the presentation of the novel development of MRFF (Magnetic Resonance Field Fingerprinting). By replacing some FISP segments with TrueFISP and FLASH segments, B0 and B1+ dependent information was added, which enabled the simultaneous generation of T1, T2, B0, B1+ and intravoxel phase dispersion maps. In the last chapter, the in-vivo reproducibility of FISP-MRF with the newly developed improvements described in the previous chapters was evaluated by scanning ten volunteers on ten scanners. T1 and T2 values varied less than 8.0% in brain compartments across scanners.Die Magnetresonanztomographie (MRT) beschränkt sich weitgehend auf die Erzeugung qualitativer Kontrastbilder anstelle von quantitativen Karten von Gewebeeigenschaften. Kürzlich wurde ein neuartiges Framework für quantitative MRT, Magnetic Resonance Fingerprinting (MRF) zur direkten Abbildung von Gewebeparametern wie der Relaxationszeiten T1 und T2 präsentiert. Bei MRF werden Gewebesignale mittels einer pseudozufällig variierenden MRT-Sequenz generiert, die unter Verwendung stark unterabgetasteter Trajektorien aufgenommen werden und daraufhin mit einer Datenbank simulierter Gewebesignale zum Zweck der Identifikation von Gewebeparametern verglichen werden. Ziel dieser Arbeit ist es, die Anfälligkeit von MRF für Unterabtastungsartefakte und Magnetfeldinhomogenitäten zu untersuchen und entsprechende Gegenmaßnahmen zu entwickeln. Da MRF auf verschiedene Arten implementiert werden kann, wurde die bis dato am häufigsten verwendete Implementierung basierend auf der FISP (Fast Imaging with Steady State Precession) Sequenz zur Analyse und als Grundlage für weitere Entwicklungen ausgewählt. Die in FISP-MRF verwendeten Einzelschuss-Spiraltrajektorien führen zu erheblichen Unterabtastungsartefakten im Bildraum. In dieser Arbeit wird deren zeitliche Variation untersucht und optimiert. Die Resultate zeigen, dass die ursprünglich vorgeschlagene Abfolge Artefakte mit ähnlichen Frequenzen wie die der Signalantworten von Geweben ergibt, was zu ortsabhängigen Parameterfehlern führt. Eine optimierte Abfolge wurde in Simulationen gefunden, die in in-vivo Experimenten bestätigt wurde. Das folgende Kapitel befasst sich mit dem Einfluss von Magnetfeldinhomogenitäten auf FISP-MRF. Hier wird gezeigt, dass variierende lokale Amplituden des HF-Feldes B1+ zu Parameterfehlern von bis zu 50% führen können, die sich durch die Messung einer B1+ Karte und Integrieren der Informationen in den Musterabgleich beheben lassen können. Eine weitere in dieser Arbeit entwickelte Strategie ist die Einführung von Akquisitionssegmenten, die gegenüber B1+ besonders sensitiv sind. Zwei Ansätze, einer mit FLASH (Fast Low-Angle Shot) und einer mit zwei um 90° phasenverschobenen Hochfrequenz-Pulsen pro TR wurden in dieser Arbeit entwickelt. Hier werden gleichzeitig Gewebeparameter- und B1+ -Karten erzeugt, wodurch gegenseitige Abhängigkeiten aufgelöst werden. In dieser Arbeit wurde auch gezeigt, dass Inhomogenitäten des statischen Magnetfelds B0 sich auf FISP-MRF auswirken können. Diese Abhängigkeit wurde analysiert und mit der relativen Phasendifferenz zwischen Spin-Ensembles und HF-Pulsen in Beziehung gesetzt. Wie in dieser Arbeit gezeigt, kann durch zusätzliches Dephasieren von Spin-Ensembles vor einem HF-Impuls der Einfluss von B0 stark vermindert werden. Im letzten Abschnitt dieses Kapitels wird die neue eigene Entwicklung MRFF (Magnetic Resonance Field Fingerprinting) präsentiert. Durch Ersetzen einiger FISP-Segmente durch TrueFISP- und FLASH-Segmente werden B0 und B1+ abhängige Informationen hinzugefügt, wodurch die gleichzeitige Erzeugung von T1, T2, B0, B1+ sowie Suszeptibilitätskarten möglich wird. Im fünften Kapitel wurde die in-vivo Reproduzierbarkeit und Wiederholbarkeit von FISP-MRF mit den in den vorhergehenden Kapiteln beschriebenen Verbesserungen durch Messungen von zehn Probanden auf insgesamt zehn Scannern evaluiert. Die T1- und T2-Werte variierten zwischen den Scannern in den Gehirnkompartimenten um weniger als 8,0%