H-Index & Metrics Best Publications

H-Index & Metrics

Discipline name H-index Citations Publications World Ranking National Ranking
Mathematics D-index 104 Citations 107,459 325 World Ranking 10 National Ranking 7
Engineering and Technology D-index 97 Citations 94,811 331 World Ranking 33 National Ranking 18

Research.com Recognitions

Awards & Achievements

2018 - Member of the National Academy of Engineering For contributions to imaging, computer vision, and graphics including level-set methods and efficient compressed sensing.

2013 - Fellow of the American Mathematical Society

2013 - John von Neumann Lecturer

2009 - Fellow of the American Academy of Arts and Sciences

2009 - SIAM Fellow For contributions to the numerical solution of partial differential equations, level set methods, and image processing.

2007 - THE J. TINSLEY ODEN MEDAL

2005 - Member of the National Academy of Sciences

1972 - Fellow of Alfred P. Sloan Foundation

Overview

What is he best known for?

The fields of study he is best known for:

  • Mathematical analysis
  • Artificial intelligence
  • Algorithm

Stanley Osher mainly focuses on Mathematical analysis, Algorithm, Level set method, Applied mathematics and Image processing. His Mathematical analysis study integrates concerns from other disciplines, such as Regularization and Nonlinear system. Stanley Osher combines subjects such as Mathematical optimization, Minification and Deblurring with his study of Algorithm.

His Level set method research incorporates elements of Level set, Level set, Curvature, Signed distance function and Vector field. His research investigates the connection between Applied mathematics and topics such as Scale space that intersect with issues in Inverse. The concepts of his Image processing study are interwoven with issues in Bounded variation and Pattern recognition.

His most cited work include:

  • Nonlinear total variation based noise removal algorithms (11267 citations)
  • Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations (11217 citations)
  • Efficient implementation of essentially non-oscillatory shock-capturing schemes,II (4161 citations)

What are the main themes of his work throughout his whole career to date?

Stanley Osher mostly deals with Mathematical analysis, Algorithm, Artificial intelligence, Applied mathematics and Computer vision. The study of Mathematical analysis is intertwined with the study of Level set method in a number of ways. Stanley Osher interconnects Level set and Level set in the investigation of issues within Level set method.

His Algorithm study combines topics in areas such as Mathematical optimization, Minification and Inverse problem. His studies link Pattern recognition with Artificial intelligence. His Applied mathematics study frequently draws parallels with other fields, such as Gradient descent.

He most often published in these fields:

  • Mathematical analysis (29.25%)
  • Algorithm (23.21%)
  • Artificial intelligence (17.74%)

What were the highlights of his more recent work (between 2017-2021)?

  • Algorithm (23.21%)
  • Artificial neural network (4.53%)
  • Applied mathematics (16.04%)

In recent papers he was focusing on the following fields of study:

His primary areas of study are Algorithm, Artificial neural network, Applied mathematics, Artificial intelligence and Gradient descent. Stanley Osher has included themes like Phase retrieval and Minification in his Algorithm study. His biological study spans a wide range of topics, including Function, Training set, Mathematical optimization and Robustness.

His Applied mathematics study incorporates themes from Dimension, Laplacian smoothing, Partial differential equation, Interpolation and Point. His studies in Artificial intelligence integrate themes in fields like Machine learning, Residual and Pattern recognition. His Regularization research is multidisciplinary, relying on both Smoothing and Image processing.

Between 2017 and 2021, his most popular works were:

  • A review of level-set methods and some recent applications (144 citations)
  • Deep relaxation: partial differential equations for optimizing deep neural networks (62 citations)
  • A Parallel Method for Earth Mover’s Distance (52 citations)

In his most recent research, the most cited papers focused on:

  • Mathematical analysis
  • Artificial intelligence
  • Algorithm

Stanley Osher spends much of his time researching Algorithm, Artificial neural network, Applied mathematics, Function and Optimal control. In the field of Algorithm, his study on Regularization overlaps with subjects such as Quantization. The study incorporates disciplines such as Saddle point, Structure, Training set and Mean field theory in addition to Artificial neural network.

The Applied mathematics study combines topics in areas such as Stability, Dimension, Metric and Laplace operator. His study in Optimal control is interdisciplinary in nature, drawing from both Curse of dimensionality, Hamilton–Jacobi equation, Differential game, Viscosity solution and Gaussian noise. His Mathematical optimization research is multidisciplinary, incorporating elements of Image processing and Type.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Best Publications

Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations

Stanley Osher;James A. Sethian.
Journal of Computational Physics (1988)

17092 Citations

Nonlinear total variation based noise removal algorithms

Leonid I. Rudin;Stanley Osher;Emad Fatemi.
Physica D: Nonlinear Phenomena (1992)

15223 Citations

Level Set Methods and Dynamic Implicit Surfaces

Stanley Osher;Ronald Fedkiw.
(2002)

6996 Citations

Efficient implementation of essentially non-oscillatory shock-capturing schemes,II

Chi-Wang Shu;Stanley Osher.
Journal of Computational Physics (1989)

6721 Citations

A level set approach for computing solutions to incompressible two-phase flow

Mark Sussman;Peter Smereka;Stanley Osher.
Journal of Computational Physics (1994)

5561 Citations

The Split Bregman Method for L1-Regularized Problems

Tom Goldstein;Stanley Osher.
Siam Journal on Imaging Sciences (2009)

4177 Citations

Weighted essentially non-oscillatory schemes

Xu-Dong Liu;Stanley Osher;Tony Chan.
Journal of Computational Physics (1994)

3162 Citations

A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method)

Ronald P Fedkiw;Tariq Aslam;Barry Merriman;Stanley Osher.
Journal of Computational Physics (1999)

2243 Citations

Level set methods: an overview and some recent results

Stanley Osher;Ronald P. Fedkiw.
Journal of Computational Physics (2001)

2138 Citations

An Iterative Regularization Method for Total Variation-Based Image Restoration

Stanley J. Osher;Martin Burger;Donald Goldfarb;Jinjun Xu.
Multiscale Modeling & Simulation (2005)

1830 Citations

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