Theme

Learning From Images

The REU/RET program focused on computational mathematics for reconstructing, analyzing, segmenting, and generating images. The research work is a collaborative effort between a group of undergraduate students, in-service math teachers, and mathematics faculty from Emory University. Four different research groups worked together on different projects under the theme “Learning from Images.” This provided undergraduate students and math teachers from around the nation numerous learning opportunities and a chance to conduct research in this area. Teachers were involved in research and able to create teaching materials that they can use in their classroom.

Seminar Schedule

Date Topic Speaker
May 24 Welcome, introductions, orientation Lars Ruthotto
June 1 Group discussions on expectations Bree Ettinger
June 7 Data and ethics Lance Waller and John Banja
June 14 Scientific Writing Bree Ettinger
June 21 Algorithmic bias Shalmali Joshi
June 28 Presentation skills: How not to give a talk Elizabeth Newman
July 5 Cloud Computing in Data Science Jeremy Jacobson
July 12 Public scholarship Carol Clark
July 19 Careers in Data Science Panel Samy Wu Fung, Clarissa Garvey, Marta D’Elia
July 26 Summary and reflection Bree Ettinger

Cohort Activities

To facilitate interactions across the teams and interactions with other faculties, our site emphasizes cohort activities. Even though the program ran virtually this year, the mentors and participants engaged in various formats. We held daily writing labs, midterm presentations, ad-hoc talks on various topics, and social events. The latter were organized by the participants themselves who got really creative and organized different virtual events such as reversi and jack box games, movie nights, chopped night, hot-takes presentations etc.

Projects

Learning from Images

A Tensor SVD-based Classification Algorithm Applied to fMRI Data
Tensors are a a much better way to store and analyze multidimensional data than traditional, matrix-based representation. However, generalizations of effective numerical techniques for extracting features from matrices such as the Singular Value Decomposition to tensors are neither straightforward nor uniquely defined. Those techniques are crucial to identify relationships in high-dimensional data. In this project, we study tensor SVDs, propose a projection-based classification algorithm, and experiment with the four-dimensional StarPlus fMRI dataset.
Dec 14, 2021
Undergraduate students and teacher develop segmentation methods for diagnosing Chiari Malformation
Our group explored two methods - a machine learning method and an atlas-based image registration method - to automatically identify the cerebellum and brain stem in magnetic resonance image (MRI) data. Identifying these two brain regions is needed to analyze DENSE MRI data and quantify the brain movement caused by the subject’s heart beat. This in turn can help determine whether or not a subject has a Chiari Malformation. We compared the strengths and weaknesses of both methods, and how they might work in the future to improve Chiari diagnosis.
Dec 14, 2021
New algorithm helps make portable CT machine images clearer
Our team has devised a way to improve point-of-care tomographic imaging and thereby making medical diagnoses more effectively. The work behind this new algorithm relies heavily upon mathematical techniques that connect numerical linear algebra with optimization methods.
Dec 14, 2021
Efficient Determinant Estimators for Potential Flow Generators
Our team developed efficient numerical linear algebra techniques to improve generative models based on potential flows. We derive a preconditioner from the stochastic Lanzcos quadratures and found that it reduced the number of conjugate gradient (CG) iterations that CG requires to converge.
Dec 14, 2021
From Images to Patient-Specific Models in Cardiology
The role of mathematical modeling in clinics is particularly evident in cardiology, as computational mechanics for many historical reasons is a mature field of applied mathematics; on the other hand, many important cardiovascular pathologies have a significant mechanical component, in terms of fluid, structure and their interactions. The clinical impact of mathematical models strongly relies on reconstructing patient geometries to customize and personalize numerical simulations. Advances in medical image processing made over the last two decades have enabled virtual patient-specific models. A key step of the processing pipeline in Cardiology is the extraction of complex vascular geometries like an aortic dissection from medical images (typically, Computed Tomographies, Magnetic Resonance, and Optical Coherence Tomography). Our team evaluated the relation between PDEs and image segmentation/reconstruction through the level set method, and compared this segmentation approach with deep learning ones based on Convolutional Neural Networks.
Dec 14, 2021