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Optimal approximation by piecewise smooth functions and associated variational problems
 Commun. Pure Applied Mathematics
, 1989
"... (Article begins on next page) The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Citation Mumford, David Bryant, and Jayant Shah. 1989. Optimal approximations by piecewise smooth functions and associated variational problems. ..."
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(Article begins on next page) The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Citation Mumford, David Bryant, and Jayant Shah. 1989. Optimal approximations by piecewise smooth functions and associated variational problems
Smooth minimization of nonsmooth functions
 Math. Programming
, 2005
"... In this paper we propose a new approach for constructing efficient schemes for nonsmooth convex optimization. It is based on a special smoothing technique, which can be applied to the functions with explicit maxstructure. Our approach can be considered as an alternative to blackbox minimization. F ..."
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Cited by 522 (1 self)
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In this paper we propose a new approach for constructing efficient schemes for nonsmooth convex optimization. It is based on a special smoothing technique, which can be applied to the functions with explicit maxstructure. Our approach can be considered as an alternative to blackbox minimization
Approximation of partially smooth functions
 Proceedings of Qikeng Lu conference, June 2006, Science in China (Ser A
, 2007
"... Abstract. In this paper we discuss approximation of partially smooth functions by smooth functions. This problem arises naturally in the study of laminated currents. ..."
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Cited by 1 (1 self)
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Abstract. In this paper we discuss approximation of partially smooth functions by smooth functions. This problem arises naturally in the study of laminated currents.
Adapting to unknown smoothness via wavelet shrinkage
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 1995
"... We attempt to recover a function of unknown smoothness from noisy, sampled data. We introduce a procedure, SureShrink, which suppresses noise by thresholding the empirical wavelet coefficients. The thresholding is adaptive: a threshold level is assigned to each dyadic resolution level by the princip ..."
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Cited by 990 (20 self)
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We attempt to recover a function of unknown smoothness from noisy, sampled data. We introduce a procedure, SureShrink, which suppresses noise by thresholding the empirical wavelet coefficients. The thresholding is adaptive: a threshold level is assigned to each dyadic resolution level
Projection Pursuit Regression
 Journal of the American Statistical Association
, 1981
"... A new method for nonparametric multiple regression is presented. The procedure models the regression surface as a sum of general smooth functions of linear combinations of the predictor variables in an iterative manner. It is more general than standard stepwise and stagewise regression procedures, ..."
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Cited by 555 (6 self)
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A new method for nonparametric multiple regression is presented. The procedure models the regression surface as a sum of general smooth functions of linear combinations of the predictor variables in an iterative manner. It is more general than standard stepwise and stagewise regression procedures
Smooth Stabilization Implies Coprime Factorization
, 1989
"... This paper shows that coprime right factorizations exist for the input to state mapping of a continuous time nonlinear system provided that the smooth feedback stabilization problem be solvable for this system. In particular, it follows that feedback linearizable systems admit such factorizations. I ..."
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Cited by 459 (62 self)
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This paper shows that coprime right factorizations exist for the input to state mapping of a continuous time nonlinear system provided that the smooth feedback stabilization problem be solvable for this system. In particular, it follows that feedback linearizable systems admit such factorizations
Mixed Optimization for Smooth Functions
"... It is well known that the optimal convergence rate for stochastic optimization of smooth functions is O(1= p T), which is same as stochastic optimization of Lipschitz continuous convex functions. This is in contrast to optimizing smooth functions using full gradients, which yields a convergence ra ..."
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Cited by 4 (0 self)
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It is well known that the optimal convergence rate for stochastic optimization of smooth functions is O(1= p T), which is same as stochastic optimization of Lipschitz continuous convex functions. This is in contrast to optimizing smooth functions using full gradients, which yields a convergence
ON ISOMORPHISMS OF ALGEBRAS OF SMOOTH FUNCTIONS
, 2003
"... Abstract. We show that for any smooth paracompact Hausdorff manifolds M and N, which are not necessarily second countable or connected, any isomorphism from the algebra of smooth (real or complex) functions on N to the algebra of smooth functions on M is given by composition with a unique diffeomorp ..."
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Cited by 10 (0 self)
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Abstract. We show that for any smooth paracompact Hausdorff manifolds M and N, which are not necessarily second countable or connected, any isomorphism from the algebra of smooth (real or complex) functions on N to the algebra of smooth functions on M is given by composition with a unique
Reconstruction and Representation of 3D Objects with Radial Basis Functions
 Computer Graphics (SIGGRAPH ’01 Conf. Proc.), pages 67–76. ACM SIGGRAPH
, 2001
"... We use polyharmonic Radial Basis Functions (RBFs) to reconstruct smooth, manifold surfaces from pointcloud data and to repair incomplete meshes. An object's surface is defined implicitly as the zero set of an RBF fitted to the given surface data. Fast methods for fitting and evaluating RBFs al ..."
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Cited by 500 (1 self)
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We use polyharmonic Radial Basis Functions (RBFs) to reconstruct smooth, manifold surfaces from pointcloud data and to repair incomplete meshes. An object's surface is defined implicitly as the zero set of an RBF fitted to the given surface data. Fast methods for fitting and evaluating RBFs
The Plenoptic Function and the Elements of Early Vision
 Computational Models of Visual Processing
, 1991
"... experiment. Electrophysiologists have described neurons in striate cortex that are selectively sensitive to certain visual properties; for reviews, see Hubel (1988) and DeValois and DeValois (1988). Psychophysicists have inferred the existence of channels that are tuned for certain visual properties ..."
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Cited by 573 (4 self)
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experiment. Electrophysiologists have described neurons in striate cortex that are selectively sensitive to certain visual properties; for reviews, see Hubel (1988) and DeValois and DeValois (1988). Psychophysicists have inferred the existence of channels that are tuned for certain visual properties; for reviews, see Graham (1989), Olzak and Thomas (1986), Pokorny and Smith (1986), and Watson (1986). Researchers in perception have found aspects of visual stimuli that are processed preattentively (Beck, 1966; Bergen & Julesz, 1983; Julesz & Bergen, Motion Color Binocular disparity Retinal processing Early vision Memory Higherlevel vision Etc... Retina More processing Still more processing Orientation Fig.1.1 A generic diagram for visual processing. In this approach, early vision consists of a set of parallel pathways, each analyzing some particular aspect of the visual stimulus. 1983; Treisman, 1986; Treisman & Gelade, 1980). And in computational
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