Discrete linear and nonlinear inverse problems arise from many different imaging systems, exhibiting inherent ill-posedness wherein solution sensitivity to data perturbations prevails. This sensitivity is exacerbated by errors arising from imaging system components (e.g., cameras, sensors, etc.), necessitating the development of robust regularization methods to attain meaningful solutions. Our presentation commences with the exposition of distinct imaging systems, and their mathematical formalism, and subsequently introduces regularization techniques tailored for linear inverse problems. Then, we delve into the variable projection method, a powerful tool to address separable nonlinear least squares problems.

BIO: Malena Español is an Assistant Professor in the School of Mathematical and Statistical Sciences at Arizona State University. She has a Bachelor's in Applied Mathematics from the University of Buenos Aires and a Master's and PhD in Mathematics from Tufts University; she was a Postdoctoral at the California Institute of Technology before starting a faculty position at The University of Akron, where she became associate professor with tenure in 2018. Her research interests are in developing, analyzing, and applying mathematical models and numerical methods for solving problems arising in science and engineering, with focus on materials science, image processing, and medical applications. In 2018, she co-organized the Women in Math of Materials (WIMM) workshop and research community, and served as co-editor of the Springer AWM Series volume "Research in the Mathematics of Materials Science." Most recently Dr. Español is the lead organizer of AMIGAS, a summer program for graduate students in applied and computational mathematics; she is also a member of the Education Advisory Board of the Institute for Computational and Experimental Research in Mathematics (ICERM). Dr. Español was awarded the 2022 Karen EDGE Fellowship, and is a current member of the Institute for Advanced Study.