7 results on '"Naetar, Wolf"'
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2. Quantitative photoacoustic tomography with piecewise constant material parameters
- Author
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Naetar, Wolf and Scherzer, Otmar
- Subjects
Mathematics - Analysis of PDEs ,35R25, 35R30, 65J22, 92C55 - Abstract
The goal of quantitative photoacoustic tomography is to determine optical and acoustical material properties from initial pressure maps as obtained, for instance, from photoacoustic imaging. The most relevant parameters are absorption, diffusion and Grueneisen coefficients, all of which can be heterogeneous. Recent work by Bal and Ren shows that in general, unique reconstruction of all three parameters is impossible, even if multiple measurements of the initial pressure (corresponding to different laser excitation directions at a single wavelength) are available. Here, we propose a restriction to piecewise constant material parameters. We show that in the diffusion approximation of light transfer, piecewise constant absorption, diffusion and Gr\"uneisen coefficients can be recovered uniquely from photoacoustic measurements at a single wavelength. In addition, we implemented our ideas numerically and tested them on simulated three-dimensional data.
- Published
- 2014
3. The Levenberg-Marquardt Iteration for Numerical Inversion of the Power Density Operator
- Author
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Bal, Guillaume, Naetar, Wolf, Scherzer, Otmar, and Schotland, John
- Subjects
Mathematics - Analysis of PDEs ,35R30, 47J06, 35J47 - Abstract
In this paper we develop a convergence analysis in an infinite dimensional setting of the Levenberg-Marquardt iteration for the solution of a hybrid conductivity imaging problem. The problem consists in determining the spatially varying conductivity $\sigma$ from a series of measurements of power densities for various voltage inductions. Although this problem has been very well studied in the literature, convergence and regularizing properties of iterative algorithms in an infinite dimensional setting are still rudimentary. We provide a partial result under the assumptions that the derivative of the operator, mapping conductivities to power densities, is injective and the data is noise-free. Moreover, we implemented the Levenberg-Marquardt algorithm and tested it on simulated data.
- Published
- 2012
4. 6. A variational method for quantitative photoacoustic tomography with piecewise constant coefficients
- Author
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Beretta, Elena, primary, Muszkieta, Monika, additional, Naetar, Wolf, additional, and Scherzer, Otmar, additional
- Published
- 2016
- Full Text
- View/download PDF
5. Reconstruction methods for quantitative coupled physics imaging
- Author
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Naetar, Wolf
- Abstract
Hybride bildgebende Verfahren kombinieren verschiedene physikalische Modalitäten (wie z.B. elektromagnetische Wellen, Ultraschall oder elektrischen Strom) zur Produktion tomographischer Daten. Quantitative hybride Verfahren verwenden derartige bildgebende Systeme um ortsabhängige physikalische Eigenschaften der Probe (wie elektrische Leitfähigkeit, optische Absorptions- oder Streukoeffizienten) zu berechnen. Diese liefern medizinisch relevante Information. Normalerweise muss dafür ein zweiteiliges Problem gelöst werden. Im ersten Schritt werden interne Daten (wie z.B. Stromdichte, Leistungsdichte oder Initialdruck) aus Messdaten berechnet. Daran anschließend können die Materialeigenschaften aus den internen Daten berechnet werden. Dies ist eine kumulative Dissertation, welche drei Forschungsartikel zu unterschiedlichen Problemen im Themenbereich der quantitativen hybriden Verfahren enthält. In den ersten beiden Artikeln wird das Rekonstruktionsproblem in quantitativer photoakustischer Tomographie behandelt. Dies ist ein bildgebendes Verfahren, welches durch Laserpulse erzeugte Ultraschallwellen misst und daraus optische Materialeigenschaften der Probe berechnet. Im ersten Artikel wird eine Einschränkung auf stückweise konstante Materialparameter vorgeschlagen. Dadurch wird es möglich, ein sonst schlecht gestelltes Problem, die Bestimmung von Absorptions-, Streu- und Grüneisenkoeffizienten der Probe aus mehreren photoakustischen Messdaten (mit unterschiedlichen Anregungsrichtungen), zu lösen. Die Rekonstruktion basiert auf einem analytischen Verfahren, welches numerisch an simulierten Daten getestet wird. Im zweiten Artikel wird, abermals unter der Annahme, dass die Koeffizienten stückweise konstant sind, gezeigt, dass wenn der Grüneisenkoeffizient der Probe bekannt ist, ihre Absorptions- und Streukoeffizienten durch eine einzige photoakustischen Messung bestimmt werden können. Weiters wird eine variationelle Rekonstruktionsmethode welche auf der Ambrosio-Tortorelli-Approximation eines Mumford-Shah-artigen Funktionals basiert vorgestellt. Der dritte Artikel behandelt ein weiteres Problem aus dem Bereich der quantitativen hybriden Verfahren, die Bestimmung der elektrischen Leitfähigkeit aus Messungen der Leistungsdichte. Dieses Problem tritt bei Akusto-Elektrischer Tomographie und Impedanz-Akustischer Tomographie auf. Wir schlagen einen iterativen Regularisierungsansatz vor, untersuchen die Konvergenz und testen an simulierten Daten., The unifying property of coupled physics imaging methods is that they use a combination of different physical modalities (e.g., electromagnetic waves, ultrasound, electric current) to obtain tomographic data. The goal of quantitative coupled physics imaging is to utilize these methods to image (spatially varying) physical properties of the sample (such as electrical conductivity or optical absorption and scattering coefficients), which can serve as valuable diagnostic information. Generally, one has to solve a two-step inverse problem to obtain such images. First, internal data (such as current density, power density or initial pressure maps) are calculated from the measurements. Then the actual material properties are recovered from the internal data. This cumulative dissertation contains three research articles on specific problems in quantitative coupled physics imaging, all of them pertaining to the second step of the two-step inverse problem. The first two articles focus on quantitative photoacoustic tomography, an imaging method that uses laser excitations to generate ultrasound waves (which can be measured) and seeks to image optical properties of the sample. In the first article, we propose a restriction to piecewise constant parameters in order to solve an otherwise ill-posed problem, the determination of absorption, diffusion and Grüneisen coefficients from multiple photoacoustic measurements (corresponding to different illumination patterns). The reconstruction is based on an analytical procedure, which we tested on simulated data. In the second article, again assuming that the coefficients are piecewise constant, we show that if the Grüneisen coefficient is known, absorption and diffusion coefficients can be recovered from a single photoacoustic measurement. We also present a variational method (based on the Ambrosio-Tortorelli approximation of a Mumford-Shah-like functional) to recover these parameters. In the third article we consider another quantitative coupled physics imaging problem, the reconstruction of electric conductivity from power density measurements, an important problem in Acousto-Electrical and Impedance-Acoustic tomography. We propose an iterative regularization approach, analyse its convergence and test the method on simulated data.
- Published
- 2015
- Full Text
- View/download PDF
6. An investigation of the properties of dendrochronological data and dating methods
- Author
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Naetar, Wolf
- Abstract
Dendrochronology, the dating of wood based on the analysis of tree ring patterns, is of prime importance in archaeology as well as in the environmental sciences. The basis of dendrochronological dating is the correlation of climatic influence factors (such as precipitation and temperature) and tree growth, which results in a similarity of the tree ring structure (usually available in the form of so-called tree ring series, i.e., series of radially measured ring widths) in contemporary trees. Several methods for automatized dating and subsequent estimation of the statistical significance of the observed similarity have been described in the dendrochronological literature. The primary goal of this work is to present many of the commonly used methods and to improve upon them to allow for reliable dating even if little reference wood is available and the ring width sequences to date are relatively short, as it typically is the case in an archaeological context. First, the common preprocessing, comparison and significance testing methods (and slight variations of them) used for automatized dating are explained. Free parameters occurring in some of the methods are determined by optimizing the dating performance in a test set. Then, a new method for comparison of tree ring series based on concepts commonly found in machine learning or data mining is sketched. Lastly, the methods presented are tested for their practical performance. Although details have to be refined and a proper mode of statistical inference remains to be devised, the test performance of the new method is promising, effectively outperforming the traditional methods and their variations., Dendrochronologie, die Datierung von Holz anhand einer Analyse der in Baumringen enthaltenen Muster, ist von großer Bedeutung in der Archäologie und den Klimawissenschaften. Die Grundlage dendrochronologischer Datierung ist der Zusammenhang zwischen klimatischen Einflussfaktoren (wie Niederschlag und Temperatur) und Baumwachstum. Diese führt zu einer Ähnlichkeit der Ringstruktur zeitgenössischer Bäume. Die dendrochronologische Fachliteratur schlägt einige Methoden zur Datierung und anschließenden Einschätzung der statistischen Signifikanz der vorgefundenen Ähnlichkeit vor. Ein Ziel dieser Arbeit ist die Beschreibung der gängigen Datierungstechniken. Weiters wird eine neue Methode (basierend auf Konzepten, die üblicherweise zur Mustererkennung bzw. für maschinelles Lernen eingesetzt werden) vorgestellt. In einer abschließende Evaluation der praktischen Datierungsleistung der vorgestellten Methoden zeigt die neue Methode ein durchaus vielversprechendes Verhalten.
- Published
- 2010
- Full Text
- View/download PDF
7. The Levenberg–Marquardt iteration for numerical inversion of the power density operator
- Author
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Bal, Guillaume, primary, Naetar, Wolf, additional, Scherzer, Otmar, additional, and Schotland, John, additional
- Published
- 2013
- Full Text
- View/download PDF
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