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Stanley Osher

Bio: Stanley Osher is an academic researcher from University of California, Los Angeles. The author has contributed to research in topics: Level set method & Hyperbolic partial differential equation. The author has an hindex of 114, co-authored 510 publications receiving 104028 citations. Previous affiliations of Stanley Osher include University of Minnesota & University of Innsbruck.


Papers
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Journal ArticleDOI
TL;DR: This work discusses how to impose boundary conditions at irregular domains and free boundaries, as well as the extension of level-set methods to adaptive Cartesian grids and parallel architectures.

289 citations

Journal ArticleDOI
TL;DR: The method introduces an improvement called "kicking" of the very efficient method and also applies it to the problem of denoising of undersampled signals, especially essentially sparse signals, which might even be undersampling.
Abstract: : We propose and analyze an extremely fast, efficient and simple method. This method was first described with more details and rigorous theory given. The motivation was compressive sensing, which now has a vast and exciting history, which seems to have started with Candes, Donoho, et.al. Our method introduces an improvement called "kicking" of the very efficient method and also applies it to the problem of denoising of undersampled signals. The use of Bregman iteration for denoising of images began and led to improved results for total variation based methods. Here we apply it to denoise signals, especially essentially sparse signals, which might even be undersampled.

266 citations

Journal ArticleDOI
TL;DR: Both historical and most recent works focused on improving the computational accuracy of the level set method are discussed, focusing in part on applications related to incompressible flow due to both of its popularity and stringent accuracy requirements.

266 citations

Journal ArticleDOI
TL;DR: The convergence of the flow for the multiplicative noise model is demonstrated, as well as its regularization effect and its relation to the Bregman distance, which shows an excellent denoising effect and significant improvement over earlier multiplicative models.
Abstract: We are motivated by a recently developed nonlinear inverse scale space method for image denoising [M. Burger, G. Gilboa, S. Osher, and J. Xu, Commun. Math. Sci., 4 (2006), pp. 179-212; M. Burger, S. Osher, J. Xu, and G. Gilboa, in Variational, Geometric, and Level Set Methods in Computer Vision, Lecture Notes in Comput. Sci. 3752, Springer, Berlin, 2005, pp. 25-36], whereby noise can be removed with minimal degradation. The additive noise model has been studied extensively, using the Rudin-Osher-Fatemi model [L. I. Rudin, S. Osher, and E. Fatemi, Phys. D, 60 (1992), pp. 259-268], an iterative regularization method [S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin, Multiscale Model. Simul., 4 (2005), pp. 460-489], and the inverse scale space flow [M. Burger, G. Gilboa, S. Osher, and J. Xu, Commun. Math. Sci., 4 (2006), pp. 179-212; M. Burger, S. Osher, J. Xu, and G. Gilboa, in Variational, Geometric, and Level Set Methods in Computer Vision, Lecture Notes in Comput. Sci. 3752, Springer, Berlin, 2005, pp. 25-36]. However, the multiplicative noise model has not yet been studied thoroughly. Earlier total variation models for the multiplicative noise cannot easily be extended to the inverse scale space, due to the lack of global convexity. In this paper, we review existing multiplicative models and present a new total variation framework for the multiplicative noise model, which is globally strictly convex. We extend this convex model to the nonlinear inverse scale space flow and its corresponding relaxed inverse scale space flow. We demonstrate the convergence of the flow for the multiplicative noise model, as well as its regularization effect and its relation to the Bregman distance. We investigate the properties of the flow and study the dependence on flow parameters. The numerical results show an excellent denoising effect and significant improvement over earlier multiplicative models.

266 citations

Book ChapterDOI
01 Jan 2003
TL;DR: This paper presents both theoretical and experimental justification for the constrained optimization type of numerical algorithm for restoring blurry, noisy images and results involve blurry images which have been further corrupted with multiplicative noise.
Abstract: In [447, 449, 450], a constrained optimization type of numerical algorithm for restoring blurry, noisy images was developed and successfully tested. In this paper we present both theoretical and experimental justification for the method. Our main theoretical results involve constrained nonlinear partial differential equations. Our main experimental results involve blurry images which have been further corrupted with multiplicative noise. As in additive noise case of [447, 450] our numerical algorithm is simple to implement and is nonoscillatory (minimal ringing) and noninvasive (recovers sharp edges).

263 citations


Cited by
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Proceedings ArticleDOI
07 Jun 2015
TL;DR: Inception as mentioned in this paper is a deep convolutional neural network architecture that achieves the new state of the art for classification and detection in the ImageNet Large-Scale Visual Recognition Challenge 2014 (ILSVRC14).
Abstract: We propose a deep convolutional neural network architecture codenamed Inception that achieves the new state of the art for classification and detection in the ImageNet Large-Scale Visual Recognition Challenge 2014 (ILSVRC14). The main hallmark of this architecture is the improved utilization of the computing resources inside the network. By a carefully crafted design, we increased the depth and width of the network while keeping the computational budget constant. To optimize quality, the architectural decisions were based on the Hebbian principle and the intuition of multi-scale processing. One particular incarnation used in our submission for ILSVRC14 is called GoogLeNet, a 22 layers deep network, the quality of which is assessed in the context of classification and detection.

40,257 citations

Journal ArticleDOI

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08 Dec 2001-BMJ
TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

33,785 citations

01 May 1993
TL;DR: Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems.
Abstract: Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

29,323 citations

Book
23 May 2011
TL;DR: It is argued that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas.
Abstract: Many problems of recent interest in statistics and machine learning can be posed in the framework of convex optimization. Due to the explosion in size and complexity of modern datasets, it is increasingly important to be able to solve problems with a very large number of features or training examples. As a result, both the decentralized collection or storage of these datasets as well as accompanying distributed solution methods are either necessary or at least highly desirable. In this review, we argue that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas. The method was developed in the 1970s, with roots in the 1950s, and is equivalent or closely related to many other algorithms, such as dual decomposition, the method of multipliers, Douglas–Rachford splitting, Spingarn's method of partial inverses, Dykstra's alternating projections, Bregman iterative algorithms for l1 problems, proximal methods, and others. After briefly surveying the theory and history of the algorithm, we discuss applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others. We also discuss general distributed optimization, extensions to the nonconvex setting, and efficient implementation, including some details on distributed MPI and Hadoop MapReduce implementations.

17,433 citations