Stanley Osher

Stanley Osher bigraphy, stories - American mathematician

Stanley Osher : biography

April 24, 1942 –

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. He also has a daughter and a son, Kathryn and Joel, respectively.


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


  • Fellow of the American Mathematical Society, 2012., retrieved 2013-03-20.
  • 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

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
  • L1/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 L1 and L1-related optimization problems which are fundamental to the fields of compressed sensing, matrix completion, robust principal component analysis, etc.

Osher has founded (or co-founded) three successful companies:

  • (with Rudin)
  • (with Yablonovitch)

Osher has been a thesis advisor for at least 40 PhD students, 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.

Books authored

  • 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).