Math Modeling Seminar: Computational and learning methods for large-scale inverse problems

Math Modeling Seminar
Computational and learning methods for large-scale inverse problems

Dr. Mirjeta Pasha
Postdoctoral Associate
School of Mathematical and Statistical Sciences
Arizona State University

You may attend this lecture in person at 2305 Gosnell Hall or virtually via Zoom.
If you’d like to attend virtually, you may register here for Zoom link.

Abstract:
Inverse problems are ubiquitous in many fields of science such as engineering, biology, medical imaging, atmospheric science, and geophysics. Three utmost challenges on obtaining meaningful solutions to large-scale and data-intensive inverse problems are ill-posedness of the problem, large dimensionality of the parameters, and the complexity of the model constraints. In this talk, we use a combination of tools from numerical linear algebra, optimization, parameter estimation, and statistics to overcome computational challenges that arise in data-intensive inverse problems. In particular, we describe computationally efficient methods that learn optimal lp and lq norms for Lp-Lq regularization and learn optimal parameters for regularization matrices defined by covariance kernels. Further we describe some efficient methods for computing solutions with preserved edges to dynamic inverse problems, where both the quantities of interest and the forward operator change at different time instances. Numerical examples such as tomographic reconstruction and image deblurring illustrate the performance of the discussed approaches in terms of both accuracy and efficiency. Current and potential future research directions will conclude the talk.

Speaker Bio:
Dr. Mirjeta Pasha is a Postdoctoral Associate at Arizona State University. She obtained a B.S. and a M.S. in Engineering Mathematics and Computer Science from University of Tirana (Albania) in 2012 and 2014, respectively. She was a tenure-track faculty at Polytechnic University of Tirana from 2014 to 2016. In 2019 she received a M.S from Kent State University (KSU) and a Ph.D. in Applied Mathematics in 2020.  After completing her Ph.D., for a semester, she was a Visiting Assistant Professor of Computer Science at John Carroll University.
Dr. Pasha uses her computational skills to solve problems that arise in many applications in science and engineering with a particular interest in medical imaging and large-scale data analysis. She develops algorithms and numerical methods for large-scale inverse problems. Her research is strongly focused on numerical linear algebra, but she also uses techniques and tools from statistics, numerical optimization, and partial differential equations. Beyond inverse problems, she works on advancing research in areas such as tensor decompositions, learning methods, and computational statistics. She has a strong interest in developing curricula and teaching students computational math and data science skills. Read more here.

Intended Audience:
Undergraduates, graduates, and experts. Those with interest in the topic.

The Math Modeling Seminar will recur each week throughout the semester on the same day and time. Find out more about upcoming speakers on the Mathematical Modeling Seminar Series webpage.
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