Stanley Osher - Research Contributions

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:

• Cognitech (with Rudin)
• Level Set Systems
• Luminescent Technologies (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.