# Accelerating Multidimensional NMR Spectroscopy by Compressed Sensing of Hypercomplex FTs

- Speaker:
- David L. Donoho - SPECIAL GUEST LECTURE - Note unusual hour
- Date:
- Sunday, 11.6.2017, 13:30
- Place:
- Room 337 Taub Bld.
- Affiliation:
- Stanford University
- Host:
- Michael Elad

Multidimensional NMR (MDNMR) experiments are an important tool in physical chemistry,but can take a long time, in some cases weeks, to conduct. At first glance, the application looks ideal for compressed sensing because the object to be recovered is sparse and the under-sampled measurements are made in the 'Fourier' domain. Actually, MDNMR is not covered by the existing compressed sensing literature. First the 'Fourier' domain is not the classical one, but involves the so-called hypercomplex Fourier transform. Second, random undersampling is not a really sensible option, because of the structure of the actual experiment. In this talk I will review this background and review recent work with Hatef Monajemi, Jeffrey Hoch and Adam Schuyler, where we find that the now traditional structures -- for example Gaussian phase transitions, which are thought to be universal -- don't accurately describe the sparsity-undersampling relation. I will give an accurate description with we think novel and interesting structure. Short Bio: ========== David Leigh Donoho is a professor of statistics at Stanford University, where he is also the Anne T. and Robert M. Bass Professor in the Humanities and Sciences. His work includes the development of effective methods for the construction of low-dimensional representations for high-dimensional data problems (multiscale geometric analysis), developments of wavelets for de-noising and compressed sensing. Donoho did his undergraduate studies at Princeton University, graduating in 1978. His undergraduate thesis advisor was John W. Tukey. Donoho obtained his Ph.D. from Harvard University in 1983, under the supervision of Peter J. Huber. He was on the faculty of the University of California, Berkeley from 1984 to 1990 before moving to Stanford. He has been the Ph.D. advisor of at least 20 doctoral students, including Jianqing Fan and Emmanuel Candes. In 1991, Donoho was named a MacArthur Fellow. He was elected a Fellow of the American Academy of Arts and Sciences in 1992. He was the winner of the COPSS Presidents' Award in 1994. In 2001, he won the John von Neumann Prize of the Society for Industrial and Applied MathematicsIn 2002, he was appointed to the Bass professorship. He was elected a SIAM Fellow and a foreign associate of the French Academie des Sciences in 2009, and in the same year received an honorary doctorate from the University of Chicago. In 2010 he won the Norbert Wiener Prize in Applied Mathematics, given jointly by SIAM and the American Mathematical Society. He is also a member of the United States National Academy of Science. In 2012 he became a fellow of the American Mathematical Society. In 2013 he was awarded the Shaw Prize for Mathematics. In 2016, he was awarded an honorary degree at the University of Waterloo. ======================================== Refreshments will be served from 13:15 Lecture starts at 13:30