California NanoSystems Institute
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Stanley Osher, Ph.D.

Professor, Mathematics
Member, California NanoSystems Institute

Ph.D., New York University, 1966

Honors and Awards:
Nanjing University, Concurrent Professor
Society of Industrial and Applied Mathematics, Ralph E. Kleinman Award
2005 - US National Academy of Sciences, US National Academy of Sciences Electee

Professional Societies:
Society for Industrial and Applied Mathematics
American Mathematical Society

Contact Information:
Email Address:
Work Address: UCLA
Department of Mathematics
Box 951555
Los Angeles, CA 90095
Home Page:
Fax Number: (310) 206-2679
Office Phone Number: 310-825-4701
Work Phone Number: (310) 825-1758
(310) 825-9036 Assistant's phone number
Research Interests:

My research consists of developing innovative numerical methods to solve partial differential equations, especially those whose solutions have steep gradients, analysis of these algorithms and the underlying P.D.E.'s and applications to various areas of Engineering, Physics, graphics, computer vision and image processing.

Technical Research Interest:

Professor Osher and his research group work on level set methods in inverse problems and optimal design. These problems involve optimizing geometry and other quantities to achieve physically desirable results (such as maximizing band gaps in photonic crystals). The group has developed the level set method, originated by Osher and Sethian in 1987 and connected it to shape sensitivity analysis, new numerical methods and regularization of ill-posed inverse problems. The level set method has had an enormous impact on science and technology (25,000 references on Google) and this includes inverse problems and optimal design problems involving geometric objects as unknowns. The application of level set methods to such kinds of problems has not only increased the computational efficiency, but also opened completely new possibilities due to its flexibility in handling topological changes. This has led to a change of paradigm in inverse obstacle problems: instead of reconstructing geometric objects with strongly restricted topology under a variety of a priori assumptions, the aim has changed to reconstruction of rather general objects with minimal a priori knowledge. The applications include: structural optimization, e,g., the design of a dam, band structure design and photonic crystals, inclusion of detections, e. g., semiconductor contact regions, scattering and tomography problems, e.g., impedance tomography, image processing and segmentation, medical imaging and state-constrained optimal control. New, emerging areas include crack detection and nucleation.

Selected Publications:

Shi JN, Yin WT, Osher S, Sajda P, A Fast Hybrid Algorithm for Large-Scale l(1)-Regularized Logistic Regression, Journal of Machine Learning Research, 2010, 11, 713-41.
Bin Dong; Aichi Chien; Zuowei Shen; Osher, S., A new multiscale representation for shapes and its application to blood vessel recovery, SIAM Journal on Scientific Computing, 2010, 32 (4), 1724-39.
Yu Mao, Bin Dong, and Stanley Osher, A nonlinear PDE-based method for sparse deconvolution, Multiscale Model. Simul, 2010, 8 (3), 965-76.
Xiaoqun Zhang; Burger, M.; Bresson, X.; Osher, S., Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction, SIAM Journal on Imaging Sciences, 2010, 3 (3), 253-76.
Mao Y, Fahimian B, Osher S, Miao J, Development and Optimization of Regularized Tomographic Reconstruction Algorithms Utilizing Equally-Sloped Tomography, IEEE Trans Image Process, 2010, 19 (5), 1259-1268.
Tom Goldstein, Xavier Bresson, Stanley Osher , Geometric Applications of the Split Bregman Method: Segmentation and Surface Reconstruction, Journal of Scientific Computing, 2010, 45 (1-3), 272-93.
Lou YF, Zhang XQ, Osher S, Bertozzi A, Image Recovery via Nonlocal Operators, JOURNAL OF SCIENTIFIC COMPUTING , 2010, 42 (2), 185-97.
Dong B, Chien AC, Mao Y, Ye JA, Vinuela F, Osher S, Level Set Based Brain Aneurysm Capturing In 3D, Inverse Problems and Imaging, 2010, 4 (2), 241-255.
Yanovsky I, Leow AD, Lee S, Osher SJ, Thompson PM., Comparing registration methods for mapping brain change using tensor-based morphometry, Med Image Anal, 2009, 13 (5), 679-700.
Joshi SH, Marquina A, Osher SJ, Dinov I, Van Horn JD, Toga AW, Edge-Enhanced Image Reconstruction Using (TV) Total Variation and Bregman Refinement, Lect Notes Comput Sci, 2009, 5567 (2009), 389-400.
Kao, C. Y. Osher, S. Qian, J. L., Legendre-transform-based fast sweeping methods for static Hamilton-Jacobi equations on triangulated meshes, Journal of Computational Physics, 2008, 227 (24), 10209-10225.
Dong, B. Ye, J. Osher, S. Dinov, I., Level Set Based Nonlocal Surface Restoration, Multiscale Modeling & Simulation, 2008, 7 (2), 589-598.
Dong B, Chien A, Mao Y, Ye J, Osher S., Level set based surface capturing in 3D medical images, Med Image Comput Comput Assist Interv, 2008, 11 (Pt. 1), 162-9.
Gilboa, G. Osher, S., Nonlocal Operators with Applications to Image Processing, Multiscale Modeling & Simulation, 2008, 7 (3), 1005-1028.
Kang, M. Merriman, B. Osher, S., Numerical simulations for the motion of soap bubbles using level set methods, Computers & Fluids, 2008, 37 (5), 524-535.
Osher, S., Special issue on level set methods - Preface, Journal of Scientific Computing, 2008, 35 (2-3), 75-76.
Yin, W. T. Goldfarb, D. Osher, S., A comparison of three total variation based texture extraction models, Journal of Visual Communication and Image Representation, 2007, 18 (3), 240-252.
Shi, Y. G. Thompson, P. M. Dinov, I. Osher, S. Toga, A. W., Direct cortical mapping via solving partial differential equations on implicit surfaces, Medical Image Analysis, 2007, 11 (3), 207-223.
Bresson, X. Esedoglu, S. Vandergheynst, P. Thiran, J. P. Osher, S., Fast global minimization of the active Contour/Snake model, Journal of Mathematical Imaging and Vision, 2007, 28 (2), 151-167.
He, L. Kao, C. Y. Osher, S., Incorporating topological derivatives into shape derivatives based level set methods, Journal of Computational Physics, 2007, 225 (1), 891-909.
Burger, M. Frick, K. Osher, S. Scherzer, O., Inverse total variation flow, Multiscale Modeling & Simulation, 2007, 6 (2), 366-395.
Xu, J. J. Osher, S., Iterative regularization and nonlinear inverse scale space applied to wavelet-based denoising, IEEE Transactions on Image Processing, 2007, 16 (2), 534-544.
Kang, M. Shim, H. Osher, S., Level set based simulations of two-phase oil-water flows in pipes, Journal of Scientific Computing, 2007, 31 (1-2), 153-184.
Gilboa, G. Osher, S., Nonlocal linear image regularization and supervised segmentation, Multiscale Modeling & Simulation, 2007, 6 (2), 595-630.
Yin, W. Goldfarb, D. Osher, S., The total variation regularized L-1 model for multiscale decomposition, Multiscale Modeling & Simulation, 2007, 6 (1), 190-211.
Kindermann, S. Osher, S. Xu, J. J., Denoising by BV-duality, Journal of Scientific Computing, 2006, 28 (2-3), 411-444.
Burger, M. Gilboa, G. Osher, S. Xu, J. J., Nonlinear inverse scale space methods, Communications in Mathematical Sciences, 2006, 4 (1), 179-212.
Losasso, F. Fedkiw, R. Osher, S., Spatially adaptive techniques for level set methods and incompressible flow, Computers & Fluids, 2006, 35 (10), 995-1010.
Aujol, J. F. Gilboa, G. Chan, T. Osher, S., Structure-texture image decomposition - Modeling, algorithms, and parameter selection, International Journal of Computer Vision, 2006, 67 (1), 111-136.
Kadioglu SY, Sussman M, Osher S, et al., A second order primitive preconditioner for solving all speed multi-phase flows, Journal of Computational Physics, 2005, 209 (2), 477-503.
Osher S, Burger M, Goldfarb D, et al., An iterative regularization method for total variation-based image restoration, Multiscale Model. Simul, 2005, 4 (2), 460-489.
Jin S, Liu HL, Osher S, et al., Computing multi-valued physical observables for the high frequency limit of symmetric hyperbolic systems, Journal of Computational Physics, 2005, 210 (2), 497-518.
Jin S, Liu HL, Osher S, et al., Computing multivalued physical observables for the semiclassical limit of the Schrodinger equation, Journal of Computational Physics , 2005, 205 (1), 222-241.
Kindermann S, Osher S, Jones PW, Deblurring and denoising of images by nonlocal functionals, Multiscale Model. Simul, 2005, 4 (4), 1091-1115.
Kao CY, Osher S, Tsai YH, Fast sweeping methods for static Hamilton-Jacobi equations, Siam Journal on Numerical Analysis, 2005, 42 (6), 2612-2632.
Leung SY, Osher S, Global minimization of the active contour model with TV-inpainting and two-phase denoising, Lecture Notes in Computer Science: Variational, Geometric, and Level Set Methods in Computer Vision, 2005, 3752, 149-160.
Yin WT, Goldfarb D, Osher S, Image cartoon-texture decomposition and feature selection using the total variation regularized L-1 functional, Lecture Notes in Computer Science: Variational, Geometric, and Level Set Methods in Computer Vision, 2005, 3752, 73-84.
Kao CY, Osher S, Yablonovitch E, Maximizing band gaps in two-dimensional photonic crystals by using level set methods, Applied Physics B: Lasers and Optics, 2005, 81 (2-3), 235-244.
Burger M, Osher S, Xu JJ, et al., Nonlinear inverse scale space methods for image restoration, Lecture Notes in Computer Science: Variational, Geometric, and Level Set Methods in Computer Vision, 2005, 3752, 25-36.
Scherzer O, Yin WT, Osher S, Slope and G-sets characterization of set-valued functions and applications to non-differentiable optimization problems, COMM. MATH. SCI, 2005, 3 (4), 479-492.
Aujol JF, Gilboa G, Chan T, et al., Structure-texture decomposition by a TV-Gabor model, Lecture Notes in Computer Science: Variational, Geometric, and Level Set Methods in Computer Vision, 2005, 3752, 85-96.
Burger, M. Osher, S., Convergence rates of convex variational regularization, Inverse Problems, 2004, 20 (5), 1411-1421.
Kao, C. Y. Osher, S. Qian, J. L., Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations, Journal of Computational Physics, 2004, 196 (1), 367-391.
Lysaker, M. Osher, S. Tai, X. C., Noise removal using smoothed normals and surface fitting, Ieee Transactions on Image Processing, 2004, 13 (10), 1345-1357.
Cecil, T. Qian, J. L. Osher, S., Numerical methods for high dimensional Hamilton-Jacobi equations using radial basis functions, Journal of Computational Physics, 2004, 196 (1), 327-347.
Cecil, T. Osher, S. Vese, L., Numerical methods for minimization problems constrained to S-1 and S-2, Journal of Computational Physics, 2004, 198 (2), 567-579.
Memoli, F. Sapiro, G. Osher, S., Solving variational problems and partial differential equations mapping into general target manifolds, Journal of Computational Physics, 2004, 195 (1), 263-292.
Tsai, Y. H. R. Cheng, L. T. Osher, S. Burchard, P. Sapiro, G., Visibility and its dynamics in a PDE based implicit framework, Journal of Computational Physics, 2004, 199 (1), 260-290.
Gibou, F. Fedkiw, R. Caflisch, R. Osher, S., A level set approach for the numerical simulation of dendritic growth, Journal of Scientific Computing, 2003, 19 (1-3), 183-199.
Qian, J. L. Cheng, L. T. Osher, S., A level set-based Eulerian approach for anisotropic wave propagation, Wave Motion, 2003, 37 (4), 365-379.
Tsai, Y. H. R. Cheng, L. T. Osher, S. Zhao, H. K., Fast sweeping algorithms for a class of Hamilton-Jacobi equations, Siam Journal on Numerical Analysis, 2003, 41 (2), 673-694.
Tasdizen, T. Whitaker, R. Burchard, P. Osher, S., Geometric surface processing via normal maps, ACM Transactions on Graphics, 2003, 22 (4), 1012-1033.
Nishimura, I. Garrell, R. L. Hedrick, M. Iida, K. Osher, S. Wu, B. , Precursor tissue analogs as a tissue-engineering strategy, Tissue Eng, 2003, 9 Suppl 1, S77-89.
Bertalmio, M. Vese, L. Sapiro, G. Osher, S., Simultaneous structure and texture image inpainting, Ieee Transactions on Image Processing, 2003, 12 (8), 882-889.
Fedkiw, R. Liu, X. D. Osher, S., A general technique for eliminating spurious oscillations in conservative schemes for multiphase and multispecies Euler equations, International Journal of Nonlinear Sciences and Numerical Simulation, 2002, 3 (2), 99-105.
Osher, S. Cheng, L. T. Kang, M. Shim, Y. Tsai, Y. H., Geometric optics in a phase-space-based level set and Eulerian framework, Journal of Computational Physics, 2002, 179 (2), 622-648.
Cheng, L. T. Burchard, P. Merriman, B. Osher, S., Motion of curves constrained on surfaces using a level-set approach, Journal of Computational Physics, 2002, 175 (2), 604-644.