STROBE Seminar: Prof. Stan Osher and Dr. Minh Pham, “Variational methods in computational microscopy”
Title: Variational methods in computational microscopy
Presenters:
Prof. Stan Osher, Professor of Mathematics, Computer Science, Electrical Engineering and Chemical and Biomolecular Engineering, UCLA
Dr. Minh Pham, Postdoctoral Fellowship as an Assistant Adjunct Professor in the Mathematics Department, UCLA
Abstract: Many Microscopy techniques have been developed to explore atomic structures of material and biological specimens at a nano-scale. Coherent Diffractive Imaging (CDI) and Atomic Electron Tomography (AET) are the most powerful among these techniques. Mathematics, especially variational optimization, also follows and supports microscopy, helping to solve various image processing problems such as deblurring and denoising. In our latest research, variational methods can help obtain super-resolution ptychography images, marking a substantial improvement in computational microscopy and bypassing the resolution limit. While sub-pixel shifting and structured probes are two crucial keys to the super-resolution problem, total variation and l1 regularization play a significant role in reconstruction. In another research project, we explore the magnetic vector fields created in the vacancy between atoms of a magnetized material. Our analysis shows that the vector tomography needs in-plane rotation and constraint support to guarantee reconstruction. The sparsity inducing l1 minimization is the right tool to generate highly accurate support. Our variational methods have successfully solved a wide range of image processing problems. We will continue to utilize these techniques again in our upcoming research.
Prof. Osher Bio: Stan Osher received his PhD in Mathematics from New York University in 1966. He has been at UCLA since 1976. He now is a Professor of Mathematics, Computer Science, Electrical Engineering and Chemical and Biomolecular Engineering. He has been elected to the US National Academy of Science, the US National Academy of Engineering and the American Academy of Arts and Sciences. He was awarded the SIAM Pioneer Prize at the 2003 ICIAM conference and the Ralph E. Kleinman Prize in 2005. He was awarded honorary doctoral degrees by ENS Cachan, France, in 2006 and by Hong Kong Baptist University in 2009. He is a SIAM and AMS Fellow. He gave a one hour plenary address at the 2010 International Conference of Mathematicians. He also gave the John von Neumann Lecture at the SIAM 2013 annual meeting. He is a Thomson-Reuters/ Clarivate highly cited researcher-among the top 1% from 2002-present in both Mathematics and Computer Science with an h index of 123. In 2014, he received the Carl Friedrich Gauss Prize from the International Mathematics Union-this is regarded as the highest prize in applied mathematics. In 2016 he received the William Benter Prize. His current interests involve data science, which includes optimization, image processing, compressed sensing, machine learning, neural nets and applications of these techniques.
Dr. Pham Bio: Minh Pham has collaborated with Miao group since Fall 2017 when he was a Ph.D. student at UCLA Mathematics Department. He completed his Ph.D. in May 2020, and right after that he started his Postdoctoral Fellowship at UCLA as an Assistant Adjunct Professor in the Mathematics Department. His research interests lie in inverse problems, image processing, algorithm development, optimization, and deep learning. In his collaboration with Miao group, he develops algorithms in solving CDI, electron and X-ray imaging, including Ptychography and Tomography.