Consistency of Probability Measure Quantization by Means of Power Repulsion–Attraction Potentials

[1]  J. Weickert,et al.  Fast electrostatic halftoning , 2014, Journal of Real-Time Image Processing.

[2]  S. Serfaty,et al.  The Γ-Limit of the Two-Dimensional Ohta–Kawasaki Energy. Droplet Arrangement via the Renormalized Energy , 2014 .

[3]  Massimo Fornasier,et al.  Asymptotic Behavior of Gradient Flows Driven by Nonlocal Power Repulsion and Attraction Potentials in One Dimension , 2014, SIAM J. Math. Anal..

[4]  Jan-Christian Hütter.  Minimizers and Gradient Flows of Attraction-Repulsion Functionals with Power Kernels and Their Total Variation Regularization , 2013 .

[5]  J. A. Carrillo,et al.  The derivation of swarming models: Mean-field limit and Wasserstein distances , 2013, 1304.5776.

[6]  Gabriele Steidl,et al.  Quadrature Errors, Discrepancies, and Their Relations to Halftoning on the Torus and the Sphere , 2012, SIAM J. Sci. Comput..

[7]  Cyrill B. Muratov,et al.  The Gamma-limit of the two-dimensional Ohta-Kawasaki energy. II. Droplet arrangement at the sharp interface level via the renormalized energy , 2012, 1210.5098.

[8]  C. Muratov,et al.  On an Isoperimetric Problem with a Competing Nonlocal Term II: The General Case , 2012, 1206.7078.

[9]  Sören Bartels,et al.  Total Variation Minimization with Finite Elements: Convergence and Iterative Solution , 2012, SIAM J. Numer. Anal..

[10]  Dominik Wied,et al.  Consistency of the kernel density estimator: a survey , 2012 .

[11]  S. Serfaty,et al.  The Γ-Limit of the Two-Dimensional Ohta–Kawasaki Energy. I. Droplet Density , 2011, 1201.0222.

[12]  M. Fornasier,et al.  Consistency of variational continuous-domain quantization via kinetic theory , 2011, 1112.1403.

[13]  M. Cicalese,et al.  Droplet Minimizers of an Isoperimetric Problem with Long‐Range Interactions , 2011, 1110.0031.

[14]  C. Muratov,et al.  On an Isoperimetric Problem with a Competing Nonlocal Term I: The Planar Case , 2011, 1109.2192.

[15]  S. Dereich,et al.  Constructive quantization: Approximation by empirical measures , 2011, 1108.5346.

[16]  Raanan Fattal,et al.  Blue-noise point sampling using kernel density model , 2011, ACM Trans. Graph..

[17]  Joachim Weickert,et al.  Dithering by Differences of Convex Functions , 2011, SIAM J. Imaging Sci..

[18]  Joachim Weickert,et al.  Universität Des Saarlandes Fachrichtung 6.1 – Mathematik Electrostatic Halftoning Electrostatic Halftoning , 2022 .

[19]  Massimo Fornasier,et al.  Theoretical Foundations and Numerical Methods for Sparse Recovery , 2010, Radon Series on Computational and Applied Mathematics.

[20]  A. Chambolle,et al.  An introduction to Total Variation for Image Analysis , 2009 .

[21]  P. Rousseeuw,et al.  Wiley Series in Probability and Mathematical Statistics , 2005 .

[22]  Holger Wendland,et al.  Scattered Data Approximation: Conditionally positive definite functions , 2004 .

[23]  P. Gruber,et al.  Optimum Quantization and Its Applications , 2004 .

[24]  Ronald F. Gariepy.  FUNCTIONS OF BOUNDED VARIATION AND FREE DISCONTINUITY PROBLEMS (Oxford Mathematical Monographs) , 2001 .

[25]  S. Graf,et al.  Foundations of Quantization for Probability Distributions , 2000 .

[26]  Gillis Pagés,et al.  A space quantization method for numerical integration , 1998 .

[27]  R. Durrett.  Probability: Theory and Examples , 1993 .

[28]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[29]  J. Wellner,et al.  Empirical Processes with Applications to Statistics , 2009 .

[30]  Federico Toschi,et al.  Collective Dynamics from Bacteria to Crowds , 2014 .

[31]  J. Norris.  Appendix: probability and measure , 1997 .

[32]  R. Bass,et al.  Review: P. Billingsley, Convergence of probability measures , 1971 .

[33]  Ricardo Cao,et al.  Nonparametric Density Estimation , 2013 .

[34]  Stephen P. Boyd,et al.  Graph Implementations for Nonsmooth Convex Programs , 2008, Recent Advances in Learning and Control.

[35]  G. Toscani,et al.  Contractive Probability Metrics and Asymptotic Behavior of Dissipative Kinetic Equations , 2007 .

[36]  L. Ambrosio,et al.  Gradient Flows: In Metric Spaces and in the Space of Probability Measures , 2005 .

[37]  Gabriele Steidl,et al.  Fast Summation at Nonequispaced Knots by NFFT , 2003, SIAM J. Sci. Comput..

[38]  Gabriele Steidl,et al.  Fast NFFT based summation of radial functions , 2003 .

[39]  L. Ambrosio,et al.  Functions of Bounded Variation and Free Discontinuity Problems , 2000 .

[40]  Sisto Baldo,et al.  Dimension reduction in variational problems, asymptotic development in Γ-convergence and thin structures in elasticity , 1994 .

[41]  G. D. Maso,et al.  An Introduction to-convergence , 1993 .

[42]  Gianni Dal Maso,et al.  An Introduction to [gamma]-convergence , 1993 .

[43]  L. Evans.  Measure theory and fine properties of functions , 1992 .