• Source: 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
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.
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






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.




See also


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




References






External links


Osher's home page at UCLA
Stanley Osher at the Mathematics Genealogy Project
Stanley Osher publications indexed by Google Scholar

Kata Kunci Pencarian:

• Stanley Osher
• Osher (name)
• Moreau envelope
• Level-set method
• Ami Harten
• Ronald Fedkiw
• Courant Institute of Mathematical Sciences
• Institute for Pure and Applied Mathematics
• Carl Friedrich Gauss Prize
• List of people by Erdős number