Date Speaker Topic
January 18 Organizational Meeting Organizational Meeting

 

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January 25

TBA

TBA

Abstract: TBA

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February 1

TBA

TBA

Abstract: TBA

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February 8

TBA

TBA

Abstract: TBA

February 15

TBA

TBA

Abstract: TBA

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February 22

TBA

TBA

Abstract: TBA

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February 29

TBA

TBA

Abstract: TBA

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March 7

Rui Han, Louisiana State University

TBA

Abstract: TBA

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March 14 Undergraduate Math Research Symposium: Scott Fullenbaum; Vievie Romanelli; and Kevin Tang, Tufts Wasserstein Dictionary Learning & Applications; Laplacian Operators on Self-Similar Spaces; Complications of Moduli Space in Genus 1

Abstract: TBA.

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March 21

Spring Break

No Talk

Abstract: No Talk

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March 28

Eyvindur Palsson, Virginia Tech

TBA

Abstract: TBA

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April 4

Alex Powell, Vanderbilt University

April 11

TBA

TBA

Abstract: TBA

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April 18 (Joint Analysis and Computational Applied Math Seminars)

Bernadette Hahn, University of Stuttgart

In the footsteps of Allan Cormack - Dynamic (computerized) tomography

Abstract: Allan Cormack’s pioneering work published in 1963 and 1964 provided the mathematical foundations of computerized tomography (CT) and thereby the first practical method to “see into” an object without physically breaking it open. Now, 50 years later, the research field of imaging is thriving and still pushes researchers to overcome new theoretical and practical challenges. One underlying assumption in the work of Cormack is that the searched-for quantity is stationary during the acquisition of the X-ray data. However, this assumption is violated in many modern applications, e.g. due to physiological motion of a patient or while imaging engines at working stage. Such a dynamic behavior leads to inconsistent data sets and the application of standard image reconstruction techniques lead to motion artefacts which can significantly impede a reliable diagnostics. Consequently, suitable models and algorithms have to be developed in order to provide artefact free images. In particular, microlocal analysis offers a powerful tool to analyze dynamic imaging problems, thus providing deep insights about the nature of the problem. Based on such analysis, we derive numerical schemes to reduce artefacts in the reconstructed image and to improve the overall image quality. We further present an alternative strategy which treats the dynamic behavior as uncertainty in the forward model. Both reconstruction approaches are evaluated on simulated and real CT-data with different dynamic behavior.

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April 19, 3:30 PM JCC 260 (Joint Analysis and Computational Applied Math Seminars. NOTE SPECIAL DATE/TIME)

Gael Rigaud, Saarland University

A data-driven approach enhanced by neural networks to address model inexactness and motion in imaging

Abstract: The development of technologies leads to new applications, new challenges, and new issues in the field of Imaging. Two of the main challenges, namely model inexactness and motion, are tackled in this talk. Dynamic inverse problems have been vastly studied in the last decade with the initial aim to reduce the artefacts observed in a CT scan due to the movements of the patient and have been developed into broader setups and applications. Motion leads in general to model inexactness. For instance, in computerized tomography (CT), the movement of the patient alters the nature of the integration curves and therefore, intrinsically, the model itself. Since the motion is in general unknown, it implies that the model is not exactly known. However, the model inexactness can be more specific with other applications. A good example is Compton scattering imaging. Modelling the Compton scattering effect leads to many challenges such as non-linearity of the forward model, multiple scattering and high level of noise for moving targets. While the non-linearity is addressed by a necessary linear approximation of the first-order scattering with respect to the sought-for electron density, the multiple-order scattering stands for a substantial and unavoidable part of the spectral data which is difficult to handle due to highly complex forward models. Last but not least, the stochastic nature of the Compton effect may involve a large measurement noise, in particular when the object under study is subject to motion, and therefore time and motion must be taken into account. To tackle these different issues, we study in this talk two data-driven techniques, namely the regularized sequential subspace optimization and a Bayesian method based on the generalized Golub-Kahan bidiagonalization. We then explore the possibilities to mimic and improve the stochastic approach with deep neural networks. The results are illustrated by simulations.

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May 2

Robert Lemke Oliver, Tufts University

TBA

Abstract: TBA

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