Stanley Osher

• B.S., Brooklyn College, 1962
• M.S., New York University, 1964
• Ph.D., New York University, 1966

• 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
• L¹/TV based convex optimization

Osher is listed as an ISI highly cited researcher.[1]

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 L¹ and L¹-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 Ph.D. 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.

• National Academy of Engineering (NAE), 2018
• William Benter Prize in Applied Mathematics, 2016.[2]
• Carl Friedrich Gauss Prize, 2014.
• John von Neumann Lecture prize from SIAM, 2013.[3]
• Fellow of the American Mathematical Society, 2013.[4]
• Plenary speaker, International Congress of Mathematicians, 2010[5]
• American Academy of Arts and Sciences, 2009
• Fellow, Society for Industrial and Applied Mathematics (SIAM), 2009 [6]
• 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 [7]
• ICIAM Pioneer Prize, 2003 [8]
• 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 [9]
• Fulbright Fellow, 1971 [10]

• S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces, Springer-Verlag, New York (2002).
• S. Osher and N. Paragios, Geometric Level Set Methods in Imaging, Vision and Graphics, Springer-Verlag, New York (2003).
• R. Glowinski, S. Osher and W. Yin, Splitting Methods in Communication, Imaging, Science and Engineering, Springer-Verlag, New York (2017)

• James Sethian, co-developer of level-set methods.

• Osher's home page at UCLA
• Stanley Osher at the Mathematics Genealogy Project