Stanley Osher

Education

• B.S., Brooklyn College, 1962
• M.S., New York University, 1964
• Ph.D., 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 and other PDE-based image processing techniques
• Scientific computing
• Applied partial differential equations
• L¹/TV based convex optimization

Research contributions

• High resolution numerical schemes to compute flows having shocks and steep gradients, including ENO schemes, WENO schemes, 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 and related fields.
• Total variation -based image restoration and shock filters. These are pioneering - and widely used - methods for PDE based image processing and have also been used for inverse problems.
• Level-set method 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.

Honors

• National Academy of Engineering, 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, 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, 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, 1982
• Alfred P. Sloan Fellow, 1972–1974
• Fulbright Fellow, 1971

  Books authored

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