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Inverse Problems and Applications, Malena Espanol and Mirjeta Pasha, Arizona State University

Abstract:

In many physical systems, the internal structure of a material can only be observed by analyzing measurements obtained on the exterior of it. For example, we might be able to describe the electrical properties of the organs inside a human body from measurements obtained by electrodes put around the body. Another example is to characterize the different densities inside a solid material object by analyzing X-ray images of it. These are examples of inverse problems. Furthermore, these are called ill-posed inverse problems because they are very sensitive to modeling and measurement errors. Therefore, robust, reliable, and efficient regularization methods need to be developed to be able to compute fast meaningful solutions. This GAG will explore the different inverse problems that appear in science and engineering, and review some of the more standard methods and discuss the current challenges. As part of this GAG we will attend different talks showcasing the current research being done in the area of inverse problems.

What are the relevant conference themes? 

  • Inverse problems
  • Optimization
  • Uncertainty quantification

Short Biographies:

Dr. Malena I. Espanol earned her B.S. in mathematics from the University of Buenos Aires, Argentina, and M.S. and Ph.D. in mathematics from Tufts University. After graduation, Dr. Espanol was a posdoctoral scholar at the California Institute of Technology. In 2012, she started a faculty position at The University of Akron were she stayed until 2019, when she joint the School of Mathematical and Statistical Sciences at Arizona State University. Her research interests are in applied and computational mathematics. More specifically, she is interested in the development, analysis, and application of mathematical models and numerical methods for solving problems arising in science and engineering, with a focus on problems related to materials science, image processing, and medical applications. Dr. Espanol co-organizes sessions at SIAM (Society of Industrial and Applied Mathematics) conferences, served as an NSF review panelist, was an MAA Project NExT (New Experiences in Teaching) Fellow from 2012-2013, and is a managing editor of the journal Electronic Transaction on Numerical Analysis (ETNA). In 2016, she co-organized a Networking Luncheon for Women in Math of Materials (WIMM) and helped to create a research community for WIMM.

Dr. Mirjeta Pasha earned her B.S. and M.S. at University of Tirana, Albania in 2012 and 2014 respectively. She worked at Polytechnic University of Tirana until 2016 as an Assistant Professor. Dr. Pasha earned a M.S and a Ph.D. in Applied Mathematics from Kent State University in 2019 and 2020. In Albania and in the United States, she has some industry experience mostly focused on Machine Learning and Financial Software Development. Dr. Pasha will be a Postdoc Associate at Arizona State University starting August 2020. Her research interests are in Applied and Computational Mathematics. In particular, she works on inverse problems, such as image processing that arise in many areas of science and engineering. She is also interested in Dynamical Systems and Mathematical Biology. She has organized academic and social activities to empower and support women in mathematics. Dr. Pasha’s biggest supporters are her 4-years old daughter, Emily, and her husband, Edvin.

Motivation:

The BE is a great program and in particular GAGS are a great way to help and meet the participants in a more interactive way!