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

@article{Fornasier2013ConsistencyOP,
  title={Consistency of Probability Measure Quantization by Means of Power Repulsion–Attraction Potentials},
  author={M. Fornasier and J. H{\"u}tter},
  journal={Journal of Fourier Analysis and Applications},
  year={2013},
  volume={22},
  pages={694-749}
}
This paper is concerned with the study of the consistency of a variational method for probability measure quantization, deterministically realized by means of a minimizing principle, balancing power repulsion and attraction potentials. The proof of consistency is based on the construction of a target energy functional whose unique minimizer is actually the given probability measure $$\omega $$ω to be quantized. Then we show that the discrete functionals, defining the discrete quantizers as… Expand
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References

SHOWING 1-10 OF 51 REFERENCES
Optimum Quantization and Its Applications
  • 88
  • PDF
Asymptotic Behavior of Gradient Flows Driven by Nonlocal Power Repulsion and Attraction Potentials in One Dimension
  • 1
  • PDF
Convergence of probability measures
  • 3,852
  • PDF
Quadrature Errors, Discrepancies, and Their Relations to Halftoning on the Torus and the Sphere
  • 26
  • PDF
Constructive quantization: Approximation by empirical measures
  • 125
  • PDF
On an Isoperimetric Problem with a Competing Nonlocal Term II: The General Case
  • 91
  • PDF
Dithering by Differences of Convex Functions
  • 40
  • Highly Influential
  • PDF
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