# Stanley Osher

Stanley Osher (born April 24, 1942) is an American mathematician, known for his many contributions in shock capturing, level-set methods, and PDE-based methods in computer vision and image processing. Osher is a professor at the University of California, Los Angeles (UCLA), Director of Special Projects in the Institute for Pure and Applied Mathematics (IPAM) and member of the California NanoSystems Institute (CNSI) at UCLA.

## Education

* BS, Brooklyn College, 1962
* MS, New York University, 1964
* PhD, New York University, 1966

## Research interests

* Level-set methods for computing moving fronts
* Approximation methods for hyperbolic conservation laws and Hamilton–Jacobi equations
* Total variation (TV) and other PDE-based image processing techniques
* Scientific computing
* Applied partial differential equations
* L$^1$/TV-based convex optimization
Osher is listed as an ISI highly cited researcher.

## Research contributions

Osher was the inventor (or co-inventor) and developer of many highly successful numerical methods for computational physics, image processing and other fields, including:
* High resolution numerical schemes to compute flows having shocks and steep gradients, including ENO (essentially non-oscillatory) schemes (with Harten, Chakravarthy, Engquist, Shu), WENO (weighted ENO) schemes (with Liu and Chan), the Osher scheme, the Engquist-Osher scheme, and the Hamilton–Jacobi versions of these methods. These methods have been widely used in computational fluid dynamics (CFD) and related fields.
* Total variation (TV)-based image restoration (with Rudin and Fatemi) and shock filters (with Rudin). These are pioneering - and widely used - methods for PDE based image processing and have also been used for inverse problems.
* Level-set method (with Sethian) for capturing moving interfaces, which has been phenomenally successful as a key tool in PDE based image processing and computer vision, as well as applications in differential geometry, image segmentation, inverse problems, optimal design, Two-phase flow, crystal growth, deposition and etching.
* Bregman iteration and augmented Lagrangian type methods for L$^1$ and L$^1$-related optimization problems which are fundamental to the fields of compressed sensing, matrix completion, robust principal component analysis, etc.
* Overcoming the curse of dimensionality for Hamilton–Jacobi equations arising in control theory and differential games.
Osher has founded (or co-founded) three successful companies:
* Cognitech (with Rudin)
* Level Set Systems
* Luminescent Technologies (with Yablonovitch)
Osher has been a thesis advisor for at least 53 PhD students, with 188 descendants, as well as postdoctoral adviser and collaborator for many applied mathematicians. His PhD students have been evenly distributed among academia and industry and labs, most of them are involved in applying mathematical and computational tools to industrial or scientific application areas.

## Honors

* National Academy of Engineering (NAE), 2018
* William Benter Prize in Applied Mathematics, 2016.
* Carl Friedrich Gauss Prize, 2014.
* John von Neumann Lecture prize from SIAM, 2013.
* Fellow of the American Mathematical Society, 2013.
* Plenary speaker, International Congress of Mathematicians, 2010
* American Academy of Arts and Sciences, 2009
* Fellow, Society for Industrial and Applied Mathematics (SIAM), 2009
* Honorary Doctoral Degree, Hong Kong Baptist University, 2009
* International Cooperation Award, International Congress of Chinese Mathematicians, 2007
* Computational and Applied Sciences Award, United States Association for Computational Mechanics, 2007
* Docteur Honoris Causa, ENS Cachan, France 2006
* National Academy of Sciences (NAS), 2005
* SIAM Kleinman Prize, 2005
* ICIAM Pioneer Prize, 2003
* Computational Mechanics Award, Japan Society of Mechanical Engineering, 2002
* NASA Public Service Group Achievement Award, 1992
* US-Israel BSF Fellow, 1986
* SERC Fellowship (England), 1982
* Alfred P. Sloan Fellow, 1972–1974
* Fulbright Fellow, 1971

## Books authored

* Osher, Stanley (2003). Level set methods and dynamic implicit surfaces. New York: Springer. ISBN 978-0-387-22746-7. OCLC 53224633.
* Osher, Stanley (2003). Geometric level set methods in imaging, vision, and graphics. New York: Springer. ISBN 978-0-387-21810-6. OCLC 56066930.
* Glowinski, R (2016). Splitting methods in communication, imaging, science, and engineering. Cham, Switzerland: Springer. ISBN 978-3-319-41589-5. OCLC 967938355.